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[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{x}$ on the interval $x = 5$ to $x = 5$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\text{ComplexInfinity}$ on the interval $x = 2$ to $x = 11$" }, { "role": "assistant", "content": "$\\text{Arc...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (2 x)$ on the interval $x = 3$ to $x = 11$" }, { "role": "assistant", "content": "$\\int_3^{11} \\sqrt{4...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (4 x)$ on the interval $x = 3$ to $x = 7$" }, { "role": "assistant", "content": "$\\frac{1}{4} (10 E(-16)...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (3 x)$ on the interval $x = 1$ to $x = 2$" }, { "role": "assistant", "content": "$-\\sqrt{2}+\\sqrt{5}+\\...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt{2} \\sqrt{x}$ on the interval $x = 1$ to $x = 2$" }, { "role": "assistant", "content": "$\\frac{1}{2} \\...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt[3]{x}$ on the interval $x = 0$ to $x = 1$" }, { "role": "assistant", "content": "$\\, _2F_1\\left(-\\fra...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = 2 \\sqrt{-x}$ on the interval $x = 5$ to $x = 5$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = e^{-x/2}$ on the interval $x = 0$ to $x = 0$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\frac{16}{625 x^4}$ on the interval $x = 0$ to $x = 3$" }, { "role": "assistant", "content": "$\\int_0^3 \\sqr...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (4 x)$ on the interval $x = 0$ to $x = 7$" }, { "role": "assistant", "content": "$4 E(-16)+\\frac{1}{4} E...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (x)$ on the interval $x = 4$ to $x = 10$" }, { "role": "assistant", "content": "$-\\sqrt{17}+\\sqrt{101}+...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (5 x)$ on the interval $x = 2$ to $x = 11$" }, { "role": "assistant", "content": "$\\frac{1}{5} (28 E(-25...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (4 x)$ on the interval $x = 2$ to $x = 8$" }, { "role": "assistant", "content": "$\\int_2^8 \\sqrt{16 \\s...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -2^{2/3} \\sqrt[3]{x^4}$ on the interval $x = 1$ to $x = 1$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (3 x)$ on the interval $x = 2$ to $x = 12$" }, { "role": "assistant", "content": "$\\frac{1}{3} (18 E(-9)...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log \\left(-\\frac{22 x}{5}\\right)$ on the interval $x = 1$ to $x = 10$" }, { "role": "assistant", "content"...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos ^{-1}(2 x) \\cos (3 x)$ on the interval $x = 2$ to $x = 2$" }, { "role": "assistant", "content": "$0$" ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (3 x)$ on the interval $x = 3$ to $x = 4$" }, { "role": "assistant", "content": "$\\int_3^4 \\sqrt{9 \\se...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = 1-\\cos (3 x)$ on the interval $x = 3$ to $x = 3$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan ^{-1}(2 x)$ on the interval $x = 1$ to $x = 1$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (-3 x)$ on the interval $x = 2$ to $x = 8$" }, { "role": "assistant", "content": "$-\\sqrt{5}+\\sqrt{65}+...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = 2 \\sqrt{x}$ on the interval $x = 3$ to $x = 5$" }, { "role": "assistant", "content": "$-2 \\sqrt{3}+\\sqrt{30}...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sin (4 x)$ on the interval $x = 0$ to $x = 7$" }, { "role": "assistant", "content": "$\\frac{1}{4} \\sqrt{17...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (2 x)$ on the interval $x = 3$ to $x = 11$" }, { "role": "assistant", "content": "$-\\sqrt{10}+\\sqrt{122...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (x)$ on the interval $x = 1$ to $x = 4$" }, { "role": "assistant", "content": "$\\int_1^4 \\sqrt{\\sec ^...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (-2 x)$ on the interval $x = 3$ to $x = 9$" }, { "role": "assistant", "content": "$-\\sqrt{10}+\\sqrt{82}...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\infty$ on the interval $x = 4$ to $x = 14$" }, { "role": "assistant", "content": "$\\text{ArcLength}[-\\inft...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sin (x) \\left(-\\csc \\left(\\frac{x}{2}\\right)\\right)$ on the interval $x = 5$ to $x = 6$" }, { "role": "assi...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sin ^{-1}(3 x)$ on the interval $x = 3$ to $x = 3$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sqrt[3]{5} e^{-2 x} \\sqrt[3]{x}$ on the interval $x = 0$ to $x = 0$" }, { "role": "assistant", "content": "...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (-5 x)$ on the interval $x = 3$ to $x = 13$" }, { "role": "assistant", "content": "$\\sqrt{10} \\left(\\s...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (5 x)$ on the interval $x = 3$ to $x = 4$" }, { "role": "assistant", "content": "$\\frac{1}{5} (2 E(-25)+...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 1$ to $x = 8$" }, { "role": "assistant", "content": "$7$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sin (4 x)$ on the interval $x = 0$ to $x = 10$" }, { "role": "assistant", "content": "$\\frac{1}{4} \\sqrt{1...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos \\left(\\frac{x}{2}\\right)$ on the interval $x = 4$ to $x = 6$" }, { "role": "assistant", "content": "$2...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -2 x$ on the interval $x = 0$ to $x = 9$" }, { "role": "assistant", "content": "$9 \\sqrt{5}$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (-3 x)$ on the interval $x = 2$ to $x = 8$" }, { "role": "assistant", "content": "$-\\sqrt{5}+\\sqrt{65}+...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sinh (x)$ on the interval $x = 2$ to $x = 12$" }, { "role": "assistant", "content": "$i \\sqrt{2} \\left(E\\l...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\log \\left(\\frac{9 x}{2}\\right)-\\tan ^{-1}(5 x)$ on the interval $x = 3$ to $x = 8$" }, { "role": "assistant"...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sinh (3 x)$ on the interval $x = 4$ to $x = 7$" }, { "role": "assistant", "content": "$\\frac{1}{3} i \\sqrt...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (4 x)$ on the interval $x = 0$ to $x = 0$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (5 x)$ on the interval $x = 2$ to $x = 6$" }, { "role": "assistant", "content": "$\\frac{1}{5} (12 E(-25)...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tanh ^{-1}(5 x)$ on the interval $x = 2$ to $x = 3$" }, { "role": "assistant", "content": "$\\int_2^3 \\sqrt{...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (3 x)$ on the interval $x = 1$ to $x = 11$" }, { "role": "assistant", "content": "$\\sqrt{2} \\left(\\sqr...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (3 x)$ on the interval $x = 5$ to $x = 6$" }, { "role": "assistant", "content": "$\\frac{1}{3} (E(18-4 \\...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (4 x)$ on the interval $x = 1$ to $x = 7$" }, { "role": "assistant", "content": "$\\int_1^7 \\sqrt{16 \\s...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 0$ to $x = 9$" }, { "role": "assistant", "content": "$9$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sin (2 x)$ on the interval $x = 0$ to $x = 9$" }, { "role": "assistant", "content": "$\\frac{1}{2} \\sqrt{5}...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (-x)+\\log (4 x)$ on the interval $x = 1$ to $x = 11$" }, { "role": "assistant", "content": "$4 \\sqrt{5}...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sin (4 x)$ on the interval $x = 0$ to $x = 5$" }, { "role": "assistant", "content": "$\\frac{1}{4} \\sqrt{17...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (x)$ on the interval $x = 5$ to $x = 6$" }, { "role": "assistant", "content": "$E(6-\\pi |-1)-E(5-\\pi |-...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (x)$ on the interval $x = 5$ to $x = 10$" }, { "role": "assistant", "content": "$\\int_5^{10} \\sqrt{\\s...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (4 x)$ on the interval $x = 2$ to $x = 2$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (3 x)$ on the interval $x = 1$ to $x = 10$" }, { "role": "assistant", "content": "$\\int_1^{10} \\sqrt{9...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (3 x)$ on the interval $x = 0$ to $x = 3$" }, { "role": "assistant", "content": "$\\int_0^3 \\sqrt{9 \\se...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos \\left(\\frac{3 x}{2}\\right)$ on the interval $x = 1$ to $x = 1$" }, { "role": "assistant", "content": "...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log \\left(4 x^2\\right)$ on the interval $x = 3$ to $x = 7$" }, { "role": "assistant", "content": "$-\\sqrt{...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (2 x)$ on the interval $x = 0$ to $x = 6$" }, { "role": "assistant", "content": "$\\int_0^6 \\sqrt{4 \\s...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos ^{-1}(-3 x)$ on the interval $x = 4$ to $x = 4$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sinh (5 x)$ on the interval $x = 0$ to $x = 6$" }, { "role": "assistant", "content": "$-\\frac{1}{5} i \\sqr...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt{2} \\sqrt{-x}$ on the interval $x = 4$ to $x = 4$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = e^{-x}$ on the interval $x = 3$ to $x = 12$" }, { "role": "assistant", "content": "$\\frac{\\sqrt{1+e^6}}{e^3}-...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = e^{5 x^2}$ on the interval $x = 3$ to $x = 4$" }, { "role": "assistant", "content": "$\\int_3^4 \\sqrt{100 e^{1...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (3 x)$ on the interval $x = 4$ to $x = 8$" }, { "role": "assistant", "content": "$\\frac{1}{3} (6 E(-9)+E...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -5 x^2$ on the interval $x = 4$ to $x = 10$" }, { "role": "assistant", "content": "$\\frac{1}{20} \\left(-40 \\...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (4 x)$ on the interval $x = 4$ to $x = 11$" }, { "role": "assistant", "content": "$\\int_4^{11} \\sqrt{1...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos ^{-1}(2 x)$ on the interval $x = 2$ to $x = 12$" }, { "role": "assistant", "content": "$\\frac{1}{2} \\sq...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sinh ^{-1}(2 x)$ on the interval $x = 3$ to $x = 3$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (3 x)$ on the interval $x = 1$ to $x = 10$" }, { "role": "assistant", "content": "$\\int_1^{10} \\sqrt{9 ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (3 x)$ on the interval $x = 5$ to $x = 9$" }, { "role": "assistant", "content": "$\\frac{1}{3} (6 E(-9)+E...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan ^{-1}(4 x)$ on the interval $x = 3$ to $x = 10$" }, { "role": "assistant", "content": "$\\int_3^{10} \\s...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = e^{-x/2}$ on the interval $x = 3$ to $x = 4$" }, { "role": "assistant", "content": "$\\frac{\\sqrt{e+4 e^4}-\\s...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (2 x)$ on the interval $x = 0$ to $x = 3$" }, { "role": "assistant", "content": "$\\int_0^3 \\sqrt{4 \\se...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt[3]{5} \\sqrt[3]{x}$ on the interval $x = 4$ to $x = 4$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\infty$ on the interval $x = 2$ to $x = 4$" }, { "role": "assistant", "content": "$\\text{ArcLength}[-\\infty...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt[3]{\\frac{5}{2}} \\sqrt[3]{x}$ on the interval $x = 0$ to $x = 6$" }, { "role": "assistant", "content": ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (5 x)$ on the interval $x = 0$ to $x = 3$" }, { "role": "assistant", "content": "$\\frac{1}{5} (8 E(-25)+...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (4 x)$ on the interval $x = 5$ to $x = 15$" }, { "role": "assistant", "content": "$\\frac{1}{4} (24 E(-16...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (4 x)$ on the interval $x = 3$ to $x = 6$" }, { "role": "assistant", "content": "$\\int_3^6 \\sqrt{16 \\...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sinh \\left(\\frac{5 x}{2}\\right)$ on the interval $x = 1$ to $x = 4$" }, { "role": "assistant", "content":...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\frac{6561}{16} e^{-x} x^4$ on the interval $x = 5$ to $x = 11$" }, { "role": "assistant", "content": "$\\int_...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{-x}$ on the interval $x = 1$ to $x = 4$" }, { "role": "assistant", "content": "$\\frac{1}{4} \...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{-x}$ on the interval $x = 1$ to $x = 4$" }, { "role": "assistant", "content": "$\\frac{1}{4} \...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan ^{-1}\\left(4 x^5\\right)$ on the interval $x = 0$ to $x = 0$" }, { "role": "assistant", "content": "$0$...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan (3 x)$ on the interval $x = 3$ to $x = 9$" }, { "role": "assistant", "content": "$\\int_3^9 \\sqrt{9 \\se...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos \\left(\\frac{12 x}{5}\\right)$ on the interval $x = 4$ to $x = 4$" }, { "role": "assistant", "content": ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos ^{-1}(x)$ on the interval $x = 4$ to $x = 10$" }, { "role": "assistant", "content": "$\\sqrt{2} \\left(2 ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = e^{-x}$ on the interval $x = 5$ to $x = 11$" }, { "role": "assistant", "content": "$\\frac{\\sqrt{1+e^{10}}}{e^...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = 2 \\sqrt{-x}$ on the interval $x = 5$ to $x = 6$" }, { "role": "assistant", "content": "$\\sqrt{5} \\left(\\sqr...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cos (x)$ on the interval $x = 0$ to $x = 0$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log (5 x) \\cos (3 x)$ on the interval $x = 0$ to $x = 6$" }, { "role": "assistant", "content": "$\\int_0^6 \...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\log \\left(\\frac{5 x}{2}\\right)$ on the interval $x = 3$ to $x = 12$" }, { "role": "assistant", "content": ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\sin \\left(\\frac{7 x}{3}\\right)$ on the interval $x = 5$ to $x = 5$" }, { "role": "assistant", "content": ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\cosh (x)$ on the interval $x = 4$ to $x = 8$" }, { "role": "assistant", "content": "$\\sinh (8)-\\sinh (4)$" ...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = -\\tan (4 x)$ on the interval $x = 2$ to $x = 7$" }, { "role": "assistant", "content": "$\\int_2^7 \\sqrt{16 \\...
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 1$ to $x = 4$" }, { "role": "assistant", "content": "$3$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\tan ^{-1}(3 x)$ on the interval $x = 2$ to $x = 2$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = e^{-2 x}$ on the interval $x = 2$ to $x = 2$" }, { "role": "assistant", "content": "$0$" } ]
calculus
arclength
[ { "role": "system", "content": "You are a mathematics tutor. Answer the following math problem." }, { "role": "user", "content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{-x}$ on the interval $x = 3$ to $x = 6$" }, { "role": "assistant", "content": "$-\\frac{3}{4} ...
calculus
arclength