messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 14
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$x^5$"
},
{
"role": "assistant",
"content": "$\\frac{x-1024}{1280}+4$"
}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$-\\left(x-\\sqrt[3... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan ^{-1}\\left(\\frac{3 x}{2}\\right)$"
},
{
"role": "assistant",
"c... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{3} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$3^{2... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sin \\left(\\frac{x}{2}\\right)$"
},
{
"role": "assistant",
"content"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log (-3 x)$"
},
{
"role": "assistant",
"content": "$-2 (x-\\log (3)-2 ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-3 x}$"
},
{
"role": "assistant",
"content": "$\\frac{\\left(x-e^3\\r... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\frac{1}{8} e^{3 x/2} x^3$"
},
{
"role": "assistant",
"content": "$\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-2^{2/3} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$\\frac{3 ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$e^{3 x}$"
},
{
"role": "assistant",
"content": "$\\frac{\\left(x-e^3\\rig... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\frac{1}{3 x}$"
},
{
"role": "assistant",
"content": "$-72 \\left(x+\\f... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fourth order series of the inverse of the following function around 4:\n$-12 x^2$"
},
{
"role": "assistant",
"content": "$-\\frac{5 (x+12)^4}{265... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fifth order series of the inverse of the following function around 5:\n$\\sqrt{\\frac{13}{5}} \\sqrt{x^2}$"
},
{
"role": "assistant",
"content": ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-2^{2/3} \\sqrt[3]{x^3}$"
},
{
"role": "assistant",
"content": "$-\\frac... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fifth order series of the inverse of the following function around 5:\n$\\frac{1}{16 x^2}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4 \\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sinh ^{-1}(x)$"
},
{
"role": "assistant",
"content": "$\\sqrt{10} \\lef... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the sixth order series of the inverse of the following function around 6:\n$\\sqrt{2} \\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan (4 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{4 \\tan (4... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan (2 x)$"
},
{
"role": "assistant",
"content": "$\\frac{2 \\tan (2)... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sinh ^{-1}(3 x)$"
},
{
"role": "assistant",
"content": "$2 \\left(x+\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sin \\left(\\frac{9 x}{2}\\right)$"
},
{
"role": "assistant",
"content... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sin (x)$"
},
{
"role": "assistant",
"content": "$\\sec (2) (x-\\sin (2)... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\cos (2 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{i \\sqrt{x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log (x)$"
},
{
"role": "assistant",
"content": "$\\frac{3}{2} (x-\\log... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$\\log (-x)$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{3} (x-\\lo... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan (x)$"
},
{
"role": "assistant",
"content": "$\\frac{\\tan (5) (x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$e^{-5 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^{10}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the seventh order series of the inverse of the following function around 7:\n$\\frac{\\sqrt[3]{x}}{\\sqrt[3]{2}}$"
},
{
"role": "assistant",
"content... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-2^{2/3} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$-\\frac{3... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{2 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{4} e^4 \\lef... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{4 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^{12}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sqrt[3]{\\frac{10}{3}} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"conten... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{2} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\tan ^{-1}\\left(\\frac{7 x}{5}\\right)$"
},
{
"role": "assistant",
"con... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fifth order series of the inverse of the following function around 5:\n$-\\sin (3 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{x^5}{40}-\\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the seventh order series of the inverse of the following function around 7:\n$-\\tan (3 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x^7}{21}-\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log (-x)$"
},
{
"role": "assistant",
"content": "$-(x-\\log (2))^2-2 (... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan ^{-1}(3 x)$"
},
{
"role": "assistant",
"content": "$-10 \\left(x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sin ^{-1}(x)$"
},
{
"role": "assistant",
"content": "$-x$"
}
] | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{2} \\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sinh ^{-1}(5 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{2... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan (x)$"
},
{
"role": "assistant",
"content": "$\\frac{\\tan (5) (x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sin (2 x)$"
},
{
"role": "assistant",
"content": "$\\frac{1}{2} \\sec (... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$x^3$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{288} (x-8)^2+\\f... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{x}$"
},
{
"role": "assistant",
"content": "$\\left(x-\\sqrt{3}\\r... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sin (x) (-\\coth (3 x))$"
},
{
"role": "assistant",
"content": "$\\frac... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\tan ^{-1}(2 x)$"
},
{
"role": "assistant",
"content": "$5 \\left(x-\\t... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{2} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the sixth order series of the inverse of the following function around 6:\n$-243 x^5$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{3} (-1)^{4/5... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log (x)$"
},
{
"role": "assistant",
"content": "$2 (x-2 \\log (2))^2+4... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sin (4 x)$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} \\sec ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{2 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{4} e^{16} \\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log (-3 x)+\\log (-x)$"
},
{
"role": "assistant",
"content": "$-x-\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$3 \\sqrt[3]{3} \\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\cos (x)$"
},
{
"role": "assistant",
"content": "$\\csc (1) (x-\\cos (1)... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$x^5$"
},
{
"role": "assistant",
"content": "$\\frac{2}{25} (x+1)^2+\\fra... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\cosh ^{-1}(-5 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{2... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\log (3 x)$"
},
{
"role": "assistant",
"content": "$5 (x-\\log (5)-\\log... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$3 \\sqrt[3]{2} \\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\cos (5 x)$"
},
{
"role": "assistant",
"content": "$\\frac{1}{5} \\csc (... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\tan (3 x)$"
},
{
"role": "assistant",
"content": "$\\frac{x-\\tan (15)... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\tan ^{-1}(3 x)$"
},
{
"role": "assistant",
"content": "$-1130 \\left(... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{3 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^9\\r... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\tan ^{-1}\\left(\\frac{11 x}{3}\\right)$"
},
{
"role": "assistant",
"co... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\sin (4 x)$"
},
{
"role": "assistant",
"content": "$2-\\frac{1}{4} \\se... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sin ^{-1}\\left(2 x^5\\right)-\\cos ^{-1}(-4 x)$"
},
{
"role": "assistant"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\frac{1}{3 x}$"
},
{
"role": "assistant",
"content": "$16875 \\left(x+\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\log \\left(\\frac{3 x}{2}\\right)$"
},
{
"role": "assistant",
"content"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{5} \\sqrt{x^3}$"
},
{
"role": "assistant",
"content": "$-\\frac{1... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\tan \\left(\\frac{5 x}{2}\\right)$"
},
{
"role": "assistant",
"content... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{5 x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{10} e^{30} \... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$e^{-4 x}$"
},
{
"role": "assistant",
"content": "$2-\\frac{1}{4} e^8 \\le... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$e^{-4 x}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{8} e^{24} \\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$-(x-1)^2-2 (x-1)-1$"... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$-\\left(x+\\sqrt[3... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$e^{-x}$"
},
{
"role": "assistant",
"content": "$-\\frac{\\left(x-e^5\\rig... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\sqrt[3]{5} \\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$-\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sin (x)$"
},
{
"role": "assistant",
"content": "$\\sec (3) (x-\\sin (3... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-x^5$"
},
{
"role": "assistant",
"content": "$\\frac{(x-32)^2}{6400}+\\f... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$2 \\sqrt{-x}$"
},
{
"role": "assistant",
"content": "$-\\frac{1}{4} \\le... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-e^{4 x} \\sin ^{-1}(2 x)$"
},
{
"role": "assistant",
"content": "$-\\fra... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\frac{8}{27 x^3}$"
},
{
"role": "assistant",
"content": "$-\\frac{81}{... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-e^{5 x^3} \\tan ^{-1}(3 x)$"
},
{
"role": "assistant",
"content": "$\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\frac{1}{32 x^5}$"
},
{
"role": "assistant",
"content": "$-6000000000 \... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\log (3 x)$"
},
{
"role": "assistant",
"content": "$2 (x-\\log (3)-2 \\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\frac{1}{27 x^3}$"
},
{
"role": "assistant",
"content": "$-5625 \\left(x... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\sqrt{3} \\sqrt{x^2}$"
},
{
"role": "assistant",
"content": "$-\\frac{x... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\tanh \\left(3 x^5\\right)$"
},
{
"role": "assistant",
"content": "$\\fr... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\cos \\left(\\frac{x}{2}\\right)$"
},
{
"role": "assistant",
"content": ... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the fourth order series of the inverse of the following function around 4:\n$\\sin (x)$"
},
{
"role": "assistant",
"content": "$\\frac{x^3}{6}+x$"
... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$32 x^5$"
},
{
"role": "assistant",
"content": "$\\frac{(x+100000)^2}{250... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$-\\frac{1}{x}$"
},
{
"role": "assistant",
"content": "$(x+1)^2+x+2$"
}... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\log (-x)$"
},
{
"role": "assistant",
"content": "$-4 (x-2 \\log (2))-4$... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the third order series of the inverse of the following function around 3:\n$-\\sin (2 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{x^3}{12}-\\... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$-\\tan ^{-1}(4 x)$"
},
{
"role": "assistant",
"content": "$1-\\frac{17}{4... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\sqrt[3]{x}$"
},
{
"role": "assistant",
"content": "$3\\ 2^{2/3} \\left(... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the eighth order series of the inverse of the following function around 8:\n$\\sinh (3 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{5 x^7}{336... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the eighth order series of the inverse of the following function around 8:\n$\\frac{1}{x^5}$"
},
{
"role": "assistant",
"content": "$\\frac{1}{\\sqrt... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the second order series of the inverse of the following function around 2:\n$\\cos (4 x)$"
},
{
"role": "assistant",
"content": "$-\\frac{i \\sqrt{x-... | calculus | series_inverse |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the first order series of the inverse of the following function around 1:\n$\\cos (3 x)-\\tan \\left(\\frac{9 x}{2}\\right)$"
},
{
"role": "assistant",
... | calculus | series_inverse |
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