prompt list | ground_truth string |
|---|---|
[
{
"content": "Let $T$ be an invertible linear operator on a finite-dimensional vector space over a finite field. Determine whether there exists a positive integer $n$ such that $T^n = I$, where $I$ is the identity operator. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $29,577.60 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2261 |
[
{
"content": "Find a closed form for \\(a_n = \\sum_{k=0}^{n}\\binom{n}{k}(n-k)^n(-1)^k\\) using generating functions.",
"role": "user"
}
] | n! |
[
{
"content": "Let $-6 \\le x_{i} \\le 10$ for $i=1,2,3,\\ldots,10$, and $\\sum_{i=1}^{10}x_{i}=50$. Find the minimum value of $\\displaystyle\\sum_{i=1}^{10}x^2_{i}$.",
"role": "user"
}
] | 250 |
[
{
"content": "Given the function $f(x+y) = f(x)f(y)$, with $f'(0) = 11$ and $f(3) = 3$, find the value of $f'(3)$. Provide your answer as a single number.",
"role": "user"
}
] | 33 |
[
{
"content": "Let $a,$ $b,$ and $c$ be distinct real numbers such that\n\\[\\frac{a^3 + 6}{a} = \\frac{b^3 + 6}{b} = \\frac{c^3 + 6}{c}.\\]Find $a^3 + b^3 + c^3.$",
"role": "user"
}
] | -18 |
[
{
"content": "Determine the minimum number of shifts required for a group of 6 people on a ship, such that for any two distinct persons $A$ and $B$, there exists a shift where $A$ is awake while $B$ is asleep.",
"role": "user"
}
] | 4 |
[
{
"content": "Determine the height $h$ of a lamp located at the point $(-2, h)$ such that a light ray emitted from it is tangent to the circle $x^2 + y^2 = 1$ in the first quadrant and intersects the x-axis at the point $(1.25, 0)$. What is the value of $h$?",
"role": "user"
}
] | \dfrac{13}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $10,462.15 |
[
{
"content": "Given the ellipse \\( E: \\frac{x^{2}}{9}+\\frac{y^{2}}{5}=1 \\) with the left focus \\( F_{1} \\), a line \\( l \\) passing through \\( F_{1} \\) intersects the ellipse \\( E \\) at points \\( A \\) and \\( B \\). Point \\( Q \\left( -\\frac{9}{2}, 0 \\right) \\) is given. If \\( \\overrightarrow... | \pm \sqrt{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $16,532.98 |
[
{
"content": "Given that \\( \\int_{0}^{2} p(x) \\, dx = p(\\alpha) + p(\\beta) \\) holds for all polynomials \\( p(x) \\) of degree at most 3, find the value of \\( 3(\\alpha - \\beta)^2 \\).",
"role": "user"
}
] | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 17715 N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9160 |
[
{
"content": "Solve for integer values of $x$ in the equation: \\[ 3^{3x} - 3^x = (3x)! \\]",
"role": "user"
}
] | 2 |
[
{
"content": "Let $x$ be a positive real number. Determine which of the following inequalities is true:\n\n(A) $ x^{2} + \\pi^{2} + x^{2\\pi}> x\\pi+ (\\pi+x)x^{\\pi} $\n\n(B) $ x^{\\pi} + \\pi^{x}> x^{2\\pi}+ \\pi^{2x} $\n\n(C) $ \\pi x +(\\pi+x)x^{\\pi}>x^2 + \\pi^2 + x^{2\\pi} $\n\n(D) None of the above.",
... | A |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 15.19% |
[
{
"content": "Determine the support of the Dirichlet function, defined as follows: if $x$ is rational, $f(x)=0$; if $x$ is irrational, $f(x)=1$. What is the support of this function?",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Evaluate the integral \\( \\frac{1}{\\pi^2}\\int_{x=0}^1\\int_{y=\\sin^{-1} x}^{\\dfrac{\\pi}{2}}f(x,y)\\mathop{dy}\\mathop{dx} \\) where \\( f(x,y)=\\begin{cases} \\frac{y}{\\sin y} & \\text{if } y\\neq 0 \\\\ 1 & \\text{if } y=0 \\end{cases} \\). Provide the answer correct to three decimal place... | 0.125 |
[
{
"content": "Evaluate the expression: $$\\frac{1}{2^{101}}\\sum_{k=1}^{51} \\sum_{r=0}^{k-1}\\binom{51}{k}\\binom{50}{r}$$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $2,795.58 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $x=e^{At}x_0 + \int_{0}^{t}e^{A(t-\tau)}bvd\tau$ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $6,911,539.39 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.6e5 kg m/s |
[
{
"content": "Let $E$ be a compact subset of a bounded open set $\\mathcal{D},$ both of which are subsets of the real numbers. Let $f(x)$ be a differentiable function such that $f(x) = \\mathcal{O}(1)$ for all $x \\in \\mathcal{D}$. Does there exist such a function where $f'(x) \\neq \\mathcal{O}(1)$ for some $... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.40*10^3 kPa |
[
{
"content": "If $\\log_{25}(x-4)=\\frac{1}{2}$, find $\\frac{1}{\\log_{x}3}$.",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Year 0: -$62,900, Year 1: $20,194, Year 2: $22,530, Year 3: $34,281 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.02s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.41 m/s |
[
{
"content": "Let \\( P \\) and \\( Q \\) be two distinct points in the plane. Denote by \\( m(PQ) \\) the segment bisector of \\( PQ \\). Let \\( S \\) be a finite subset of the plane, with more than one element, that satisfies the following properties:\n\n1. If \\( P \\) and \\( Q \\) are in \\( S \\), then \... | 3 |
[
{
"content": "What is the range of the function $$F(x) = |x+1|+|x-5|~?$$Express your answer in interval notation.",
"role": "user"
}
] | [6,\infty) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.8483616573 |
[
{
"content": "If $X_1, X_2, \\dots, X_n$ are $KC$ subspaces of a topological space $X$, is the intersection $X_1 \\cap X_2 \\cap \\dots \\cap X_n$ also a $KC$ subspace?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 155 nm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.493 m/s^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5 cm |
[
{
"content": "Determine the spectrum of the operator $L:L^1(S^1)\\to L^1(S^1)$ defined by \\[ (Tf)(x)=\\dfrac{1}{2}\\left( f\\left( \\dfrac{x}{2}\\mod 1\\right)+f\\left( \\dfrac{x+1}{2} \\mod 1 \\right) \\right) \\] where $S^1$ is identified with $\\mathbb{R}/\\mathbb{Z}$.",
"role": "user"
}
] | \{ \lambda \in \mathbb{C} : |\lambda| \leq 1 \} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 17.5 m/s |
[
{
"content": "Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) that satisfy the following conditions:\n1. \\( \\lim_{{x \\to 0}} \\frac{f(x)}{x} = 1 \\)\n2. For all real numbers \\( x \\) and \\( y \\), \\( f(x+y) = f(x) + f(y) + 2xy \\)",
"role": "user"
}
] | x^2 + x |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | N^(+)(=O)(O^-)_2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 49.6 kJ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.5e17 m/s^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | the evaluation of each other's efforts |
[
{
"content": "Determine the radius of convergence of the power series \\( \\sum_{n=1}^{\\infty} \\frac{n^n}{n!} \\cdot (z-1)^n \\).",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.50 |
[
{
"content": "Find the conjugate harmonic function $v(x,y)$ of the function $$u(x,y)=x^4-6x^2y^2+y^4$$ given that $v(0,0)=2$. Calculate the value of $|v(1,-1)|$.",
"role": "user"
}
] | 2 |
[
{
"content": "In an ordered commutative ring $R$, consider a polynomial function $f(r)$. If $f'(r) \\geq 0$ for all $r$ in a dense subset of an interval $[r_1, r_2]$, does it follow that $f(r_2) - f(r_1) \\geq 0$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.23e-4 M |
[
{
"content": "Determine whether there exists a sequence of functions in $C^2[0,1]$ that converges in the $L^2$ norm to a function that is not in $C^2[0,1]$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "All sides of the convex pentagon $ABCDE$ are of equal length, and $\\angle A = \\angle B = 90^\\circ$. What is the degree measure of $\\angle E$?",
"role": "user"
}
] | 150^\circ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.5 g |
[
{
"content": "Given two Banach spaces $X$ and $Y$, and a bounded surjective linear operator $T: X \\to Y$, can we always find a linear map $g: Y \\to X$ such that $T \\circ g = \\text{Id}_Y$?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the remainder when \\(11^{2402}\\) is divided by \\(3000\\).",
"role": "user"
}
] | 121 |
[
{
"content": "Evaluate the integral \\( \\int_0^{2 \\pi} \\frac{\\sin x}{1+\\frac{1}{2}\\cos x} \\, dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let $U$ be a non-empty open subset of $\\mathbb{C}$. Consider a holomorphic function $f$ defined by the series \\( f(z) = \\sum_{n=0}^\\infty a_n e^{2\\pi i nz} \\), where \\( a_n \\in \\mathbb{C} \\) for every \\( n \\) and \\( z \\in U \\). If \\( f(z) = 0 \\) for every \\( z \\in U \\), must it... | Yes |
[
{
"content": "In \\( \\triangle ABC \\), the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are \\(a\\), \\(b\\), and \\(c\\) respectively. Given that \\(a^{2} + b^{2} = 2019c^{2}\\), find the value of \\(\\frac{\\cot C}{\\cot A+\\cot B}\\).",
"role": "user"
}
] | 1009 |
[
{
"content": "Let $A$ be a real $3 \\times 3$ matrix such that $A^3 = I$ and $A \\neq I$. Determine the trace of $A$. \\( \\text{(Express your answer as a single integer.)} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 700 N/C |
[
{
"content": "Determine the angle \\(\\theta\\) that minimizes the expression \\(\\max(\\cos^2(\\theta), 1-\\cos^2(45^\\circ-\\theta))\\).",
"role": "user"
}
] | 67.5^\circ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | K_4 = \sqrt{\frac{K_2K_1^2}{K_3^6}} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 125% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.46% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $50.65 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | incomplete dominance |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 1} \\left(\\frac{f(x)}{f(1)}\\right)^{1/\\log(x)} \\] given that \\( f(x) \\) is differentiable at \\( x=1 \\) and \\( f(1) > 0 \\).",
"role": "user"
}
] | e^{\frac{f'(1)}{f(1)}} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1. Jenna's computer is working fine, but she wants to purchase a new model.
2. Jenna uses her computer recreationally and wants to be able to listen to music with her friends in two days when they visit.
3. Jenna's work computer broke, and she needs a new one or else she cannot work. |
[
{
"content": "Let $x$ and $y$ be real numbers such that $a + b = 6$, $ax + by = 10$, $ax^2 + by^2 = 24$, and $ax^3 + by^3 = 62$. Determine the value of $ax^4 + by^4$.",
"role": "user"
}
] | 162 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2363.22 ft |
[
{
"content": "In the expansion of \\((1 + x)^n (1 + y)^n (1 + z)^n\\), determine the sum of the coefficients of the terms of degree \\(r\\).",
"role": "user"
}
] | \dbinom{3n}{r} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Fe2O3 |
[
{
"content": "Let $n$ be a given positive integer, and let $a_1, a_2, \\ldots, a_n$ be non-negative numbers such that $a_1 + a_2 + \\cdots + a_n = n$. Determine the maximum value of the function \\[ f(a_1, a_2, \\ldots, a_n) = (n^{n-1} - 1) \\sqrt[n]{a_1 a_2 \\cdots a_n} + \\sqrt[n]{\\frac{a_1^n + a_2^n + \\cdo... | n^{n-1} |
[
{
"content": "Determine the number of ways to arrange $2n$ distinct objects in a circle such that each object is adjacent to exactly two other objects, and no two adjacent objects are the same.",
"role": "user"
}
] | (2n - 1)! |
[
{
"content": "Determine the number of distinct monic quadratic trinomials with integer coefficients such that they have at least one root, all roots are powers of 11 with non-negative integer exponents, and the absolute value of their coefficients does not exceed \\(1331^{38}\\).",
"role": "user"
}
] | 3363 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1402033.896 ft-lbs |
[
{
"content": "Find the interval of convergence for the series \\( \\sum_{n=1}^{\\infty}\\frac{x^n}{n^x} \\).",
"role": "user"
}
] | (-1, 1) |
[
{
"content": "Evaluate the contour integral \\( \\int_{\\gamma(0,1)} \\frac{\\cos(z)}{z^2}dz \\), where \\( \\gamma(0,1) \\) is the circular contour defined by \\( z = e^{it} \\) for \\( 0 \\leq t \\leq 2\\pi \\).",
"role": "user"
}
] | 0 |
[
{
"content": "In a semicircle with diameter AC, a triangle ABC is inscribed. Points E and F are the midpoints of arcs AB and BC, respectively. Lines EC and FA intersect AB and BC at points H and G, respectively, such that EH and FG are perpendicular to AC. Given that HG = 4 meters, find the radius of the circle... | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.62% |
[
{
"content": "The complex number \\( \\left(\\sqrt{\\frac{1}{2} + \\frac{\\sqrt{3}}{2}i}\\right)^{1/3} \\) can be expressed in polar form as \\( r(\\cos x + i\\sin x) \\) with \\( r < 0 \\). Find the smallest positive value of \\( x \\) in degrees.",
"role": "user"
}
] | 10 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $519 |
[
{
"content": "Determine the automorphism group of the group \\(\\mathbb{Z}_2 \\oplus \\mathbb{Z}_2\\).",
"role": "user"
}
] | S_3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2350 km |
[
{
"content": "Are all compact subsets of \\( \\mathbb{R}^{\\mathbb{R}} \\) separable? Consider \\( \\mathbb{R} \\) with its usual topology and \\( \\mathbb{R}^{\\mathbb{R}} \\) with the topology of pointwise convergence. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.35% |
[
{
"content": "Is the subspace of $C[-1,1]$ consisting of odd functions closed under the supremum norm?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the values of $a$ and $b$ given the following limits:\n\n\\[ a = \\lim_{x\\rightarrow0}\\left[\\lim_{y\\rightarrow0}\\frac{1-\\cos(x)}{\\sin(x)+\\sin(y)}\\right] \\]\n\\[ b = \\lim_{y\\rightarrow0}\\left[\\lim_{x\\rightarrow0}\\frac{1-\\cos(x)}{\\sin(x)+\\sin(y)}\\right] \\]\n\nChoose th... | D |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.0 mph |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $134,000 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $280,830 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -0.25 N s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.0 kg |
[
{
"content": "Evaluate the Stieltjes integral \\( \\int_{0}^3 x^2 \\, d\\alpha \\), where \\( \\alpha(x) = x+1 \\) for \\( 0 \\le x \\le 1 \\) and \\( \\alpha(x) = x^2+2 \\) for \\( 1 < x \\le 3 \\).",
"role": "user"
}
] | \dfrac{124}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1. Argon (Ar)
2. Chloride ion (Cl-)
3. Sulphide ion (S2-) |
[
{
"content": "Calculate the surface integral of the sphere defined by the equation \\(x^2 + y^2 + z^2 = 1\\) that lies between the two cones \\(z = \\sqrt{x^2 + y^2}\\) and \\(z = -\\sqrt{x^2 + y^2}\\).",
"role": "user"
}
] | 2\sqrt{2}\pi |
[
{
"content": "Find the last eight digits of the binary representation of \\(27^{1986}\\).",
"role": "user"
}
] | 11011001 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $41.64 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | a/6 |
[
{
"content": "Evaluate the surface integral of the function \\( G(x,y,z) = x + y + z \\) over the surface cut from the first octant by the plane \\( 2x + 2y + z = 2 \\).",
"role": "user"
}
] | 2 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.