prompt list | ground_truth string |
|---|---|
[
{
"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... | 18.58 nF |
[
{
"content": "Evaluate the integral \\( \\int_C \\frac{x^2 - y^2}{(x^2 + y^2)^2} \\, dx + \\frac{2xy}{(x^2 + y^2)^2} \\, dy \\) where \\( C \\) is a simple closed loop containing the origin.",
"role": "user"
}
] | 0 |
[
{
"content": "Prove that \\((\\log(n))^{\\log(\\log(n))} = O(n)\\).",
"role": "user"
}
] | (\log(n))^{\log(\log(n))} = O(n) |
[
{
"content": "Does a group $G$ of order $n$, where $n$ is divisible by distinct primes $p$ and $q$, necessarily have a subgroup of order $p \\cdot q$? Answer yes or no.",
"role": "user"
}
] | No |
[
{
"content": "Determine all real numbers \\( \\alpha \\) for which there exists a matrix \\( A \\in M_{2005}(\\mathbb{R}) \\) such that \\( 5A^2 + (6\\alpha - 2)A + (2\\alpha^2 - 2\\alpha + 1)I = 0 \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Find the value of \\( \\limsup\\limits_{n\\rightarrow\\infty}\\left\\{\\frac{p_{m+1}}{p_m}\\middle|m\\in \\mathbb{N},m\\geq n\\right\\} \\), where \\( p_i \\) is the \\( i \\)-th prime number.",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the triple integral \\(\\int_{\\Omega}(x+y+z)^2xyz \\, dxdydz\\) over the region \\(\\Omega\\) defined by \\(0\\leq x+y+z\\leq 1\\), \\(1\\geq x\\geq0\\), \\(1\\geq y\\geq 0\\), and \\(1\\geq z\\geq 0\\), using the change of variables: \\(x = v-w\\), \\(y = w-u\\), \\(z = u\\).",
"rol... | \dfrac{1}{960} |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty} \\int_0^{\\infty} \\frac{\\ln(n+x)}{n}e^{-x} \\cos(x)\\, dx.$$",
"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... | -0.27 m/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... | 0.373 grams |
[
{
"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... | 100.345 m |
[
{
"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... | 0.028 m |
[
{
"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... | 1.59 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... | 28.7 g |
[
{
"content": "Determine the map $q_*$ on the $n$-th homology level for the quotient map $q: S^n \\rightarrow S^n \\vee S^n$, where $q$ identifies the equator of $S^n$. Express $q_*$ as a map from $\\mathbf{Z}$ to $\\mathbf{Z} \\oplus \\mathbf{Z}$.",
"role": "user"
}
] | (1, 1) |
[
{
"content": "In a box, there are eight real coins and two fake coins, with the fake coins having a different weight than the real ones. You randomly select a pair of coins without replacement from the ten coins, and then select another pair from the remaining eight coins. What is the probability that all four ... | \dfrac{15}{19} |
[
{
"content": "Find all solutions to\n\\[x^2 + 4x + 4x \\sqrt{x + 3} = 13.\\]Enter all the solutions, separated by commas.",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the sum of the infinite series \\( \\sum_{k=1}^{\\infty} \\frac{1}{k(k+2)(k+4)} \\).",
"role": "user"
}
] | \dfrac{11}{96} |
[
{
"content": "Determine the Pfaffian of the curvature tensor for a 2-dimensional oriented Riemannian manifold.",
"role": "user"
}
] | K \, dA |
[
{
"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... | 0.70 |
[
{
"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... | M3 |
[
{
"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... | 161.25 W/m^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... | 2243.96 atm |
[
{
"content": "Given a compact Riemann surface $S$ and two distinct points $p$ and $q$ on it, determine whether it is always possible to find a meromorphic function $f$ on $S$ such that $f(p) = 0$ and $f(q) \\neq 0$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the length of a normal chord in the parabola \\(y^2 = 4x\\) that forms a right angle with the vertex \\(O(0,0)\\).",
"role": "user"
}
] | 6\sqrt{3} |
[
{
"content": "Let $A \\in \\mathbb{R}^{n \\times n}$ be a matrix with $\\|A\\| < 1$, and let $\\vec{b} \\in \\mathbb{R}^{n}$ be an eigenvector of $A$ corresponding to the largest eigenvalue $0 < \\lambda < 1$. Is it possible for $\\vec{b}$ to also be an eigenvector of $(I-A)$ corresponding to the largest eigenv... | 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... | At x=0, dT/dt = -28.35 C/s; At x=4, dT/dt = 25.14 C/s |
[
{
"content": "Describe the image of the function \\( f(z) = z^4 \\) for \\( z \\) in the quarter-disk defined by \\( |z| \\leq 1 \\) and \\( 0 \\leq \\text{Arg}(z) \\leq \\frac{\\pi}{2} \\).",
"role": "user"
}
] | |w| \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... | 7.49% |
[
{
"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... | Model 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... | $6,509.53 |
[
{
"content": "The function $f(x)$ is not defined at $x=0$, but for all non-zero real numbers $x$, the equation $f(x) + 2 f\\left(\\frac{1}{x}\\right) = 3x$ holds. Determine the number of real solutions to the equation $f(x) = f(-x)$. Choose the correct option:\n\nA. Exactly one real solution\nB. Exactly two rea... | B |
[
{
"content": "Five people own a safe with several locks arranged in parallel, meaning all locks must be opened to access the safe. Each lock can have any number of keys. Determine the minimum number of locks required so that any combination of at least 3 people can open the safe.",
"role": "user"
}
] | 10 |
[
{
"content": "Find the conditional expectation \\( E(X|X>Y) \\) where \\( X \\) and \\( Y \\) are independent and uniformly distributed on the interval \\((0,1)\\).",
"role": "user"
}
] | \dfrac{2}{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... | 8.88 grams |
[
{
"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... | 1.67 |
[
{
"content": "Determine all functions \\( f : [0,1] \\to [0,1] \\) that satisfy the equation \\( |f(x)-f(y)|=|x-y| \\) for all \\( x, y \\in [0,1] \\), with the conditions \\( f(0) = 1 \\) and \\( f(1) = 0 \\).",
"role": "user"
}
] | f(x) = 1 - 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... | 7332 N |
[
{
"content": "Calculate the residues of the meromorphic function \\( f(z) = \\frac{e^{2z} + 2e^z}{(1-e^{-z})^2} \\) at its singularities located at \\( z = 2\\pi \\mathrm{i} k \\) for \\( k \\in \\mathbb{Z} \\).",
"role": "user"
}
] | 7 |
[
{
"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... | marketing plan |
[
{
"content": "How many ways are there to divide 30 objects, consisting of 5 pears, 5 apples, 5 doughnuts, 5 lollipops, 5 chocolate cats, and 5 candy rocks, into two unordered piles of 15 objects each?",
"role": "user"
}
] | 2166 |
[
{
"content": "Given integers $E$ and $W$, consider $S$ as the set of all values $(cE) \\mod W$, for all integers $c$ from 0 to $W$. Determine the maximum number of times a value can appear in the set $S$.",
"role": "user"
}
] | \gcd(E, W) + 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... | 3.37e+23 |
[
{
"content": "Evaluate the double integral \\( \\iint\\limits_D (10x^2+39xy+14y^2)^2 \\, dx \\, dy \\) over the region \\( D \\) bounded by the lines \\( 2x+7y=1 \\), \\( 2x+7y=-1 \\), \\( 5x+2y=3 \\), and \\( 5x+2y=-3 \\).",
"role": "user"
}
] | \dfrac{12}{31} |
[
{
"content": "Suppose $g$ is a continuous function defined on $[b, +\\infty)$. If the integral $\\int_b^{+\\infty} g(x) \\, dx$ converges, prove or disprove that $\\lim_{n\\to\\infty}\\int_n^\\infty g(x)\\, dx=0$.",
"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... | 40.05 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 eV |
[
{
"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... | 24% |
[
{
"content": "Let $\\mu$ be a Borel probability measure on $\\mathbb{R}^d$, and let $\\phi, \\psi: \\mathbb{R}^d \\rightarrow \\mathbb{R}$ be measurable mappings defined $\\mu$-almost everywhere. If, for every bounded Borel function $f$ on $\\mathbb{R}$, the equality \\[\\int_{\\mathbb{R}^d} f \\circ \\phi \\, ... | 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... | 9312.85 |
[
{
"content": "Determine the number of combinations where 16 trials are evenly distributed among 4 individuals, each conducting 4 trials, such that there are a total of 5 successes across all trials and no individual has more than 2 successes in their trials.",
"role": "user"
}
] | 3264 |
[
{
"content": "Determine the number of positive integers, each with exactly \\(2^{2005}\\) digits, where each digit is either 7 or 8, such that among any two chosen integers, at most half of their corresponding digits are the same.",
"role": "user"
}
] | 2^{2006} |
[
{
"content": "Let $G$ be a group and $X$ be a G-set. Determine whether the following statement is true or false: If $a \\cdot x = b \\cdot x$ for some $x \\in X$, then $a = b$ in $G$. Justify your answer.",
"role": "user"
}
] | False |
[
{
"content": "Calculate the limit: $$\\lim_{x \\to 0} \\left(1+\\frac {1-\\cos x} {x} \\right)^\\frac{1}{x}$$",
"role": "user"
}
] | \sqrt{e} |
[
{
"content": "Let $f(x) = x^3 + \\log_{2}(x + \\sqrt{x^2 + 1})$. For any real numbers $a$ and $b$ satisfying $a + b \\geqslant 0$, determine which of the following is true for $f(a) + f(b) \\geqslant 0$:\n\n(A) A sufficient and necessary condition\n\n(B) A sufficient but not necessary condition\n\n(C) A necessa... | A |
[
{
"content": "Determine whether the following statement is true or false: For every natural number \\( k \\), there exists a natural number \\( m \\) such that \\( k!\\pi + \\frac{\\pi}{6} \\leq m! \\leq k!\\pi + \\frac{5\\pi}{6} \\).",
"role": "user"
}
] | False |
[
{
"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... | 3120 ft-lb |
[
{
"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... | R$\theta$ln(Vf/Vi)+R$\theta$B(1/Vf-1/Vi) |
[
{
"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... | 729 g |
[
{
"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... | {\dfrac{(v_0t) + (v_10.5(T - t) + v_20.5(T - t))}{T} |
[
{
"content": "Find $A+B$ (in base 10), given the following addition problem \\[ \\begin{array}{c@{}c@{\\;}c@{}c@{}c@{}c}& & & 4 & A & B_{6}\\\\ &+& & & 4 & 1_{6}\\\\ \\cline{2-6}& & & 5 & 3 & A_{6}\\\\ \\end{array} \\]",
"role": "user"
}
] | 9 |
[
{
"content": "Given invertible matrices $A$ and $B$, and matrices $X$ and $Y$ of size $n \\times n$, if $A^k X = B^k Y$ for $k=1,2,...,2n$, does it follow that $X = Y$? Provide a justification for your answer.",
"role": "user"
}
] | X = Y |
[
{
"content": "In a regular quadrilateral pyramid \\(S A B C D\\) with base \\(A B C D\\), all edges are of equal length. Plane \\(\\alpha\\) is perpendicular to line \\(S A\\), and plane \\(\\beta\\) is parallel to line \\(C D\\). Find the smallest possible angle between planes \\(\\alpha\\) and \\(\\beta\\).",... | 30^\circ |
[
{
"content": "Determine the number of ways to select 13 numbers from the set \\( \\{1, 2, 3, 4, 5\\} \\) such that their arithmetic mean is 4.6.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following statement is true or false: If $f:(a,b)\\to\\mathbb{R}$ is derivable on a dense subset $D \\subset (a,b)$, then $f$ is derivable on $(a,b)$. Provide a justification for your answer.",
"role": "user"
}
] | B |
[
{
"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... | {
"Sales": {
"South": 446000,
"Central": 600000,
"North": 540000,
"Total": 1586000
},
"Less: Variable Costs": {
"South": 209620,
"Central": 234000,
"North": 259200,
"Total": 702820
},
"Contribution": {
"South": 236380,
"Central": 366000,
"North": 280800,
"Total": 883180
},
"Less: Traceabl... |
[
{
"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... | cb[t+1] = cb[t] + (ca1[t+1]*k2 + ca[t+1]*k1)*delt |
[
{
"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... | 1.4 times the radius of the Earth |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{1} (1-x^{\\frac{1}{a}})^{-\\frac{1}{2}} \\, dx \\) as \\( a \\to 0 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate \\( \\lim_{n\\to\\infty}\\int_0^2f(n-x)\\,dx \\) given that \\( f \\) is continuous on \\([0, \\infty)\\) and \\( \\lim_{x \\to\\infty}f(x)=L \\).",
"role": "user"
}
] | 2L |
[
{
"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... | $51.85 |
[
{
"content": "Let the left and right foci of a hyperbola be \\( F_{1}, F_{2} \\), and the left and right vertices be \\( M, N \\). If the vertex \\( P \\) of triangle \\( \\triangle P F_{1} F_{2} \\) lies on the hyperbola, determine the location of the point of tangency of the incircle of \\( \\triangle P F_{1}... | C |
[
{
"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... | -270 J |
[
{
"content": "Evaluate the double integral \\(\\int_{-1}^1 \\int_{-1}^1 \\sqrt{\\frac{1+x-y-xy}{1-x+y-xy}} \\,dx\\,dy \\).",
"role": "user"
}
] | \pi^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... | 9.62% |
[
{
"content": "Let \\( n \\in \\mathbb{N}_{\\geq 2} \\). For any real numbers \\( a_1, a_2, \\ldots, a_n \\), denote \\( S_0 = 1 \\) and for \\( 1 \\leq k \\leq n \\), denote \\[ S_k = \\sum_{1 \\leq i_1 < i_2 < \\ldots < i_k \\leq n} a_{i_1} a_{i_2} \\ldots a_{i_k}. \\] Find the number of \\( n \\)-tuples \\((a... | 2^{n-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... | 3Ag{eq}_2 S {/eq} + 2Al + 6H{eq}_2 O {/eq} -> 2Al(OH){eq}_3 {/eq} + 3H{eq}_2 S {/eq} + 6Ag |
[
{
"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... | 2237 |
[
{
"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... | 1.92e-5 |
[
{
"content": "Determine whether there exist an integer $k$ and two infinite sequences of natural numbers $\\{a_n\\}_{n=1}^{\\infty}$ and $\\{b_n\\}_{n=1}^{\\infty}$, with $0\\leq b_n<a_n$ for all $n$, such that $k\\equiv b_n \\pmod{a_n}$ for all $n$. Provide a justification for your answer.",
"role": "user"... | Yes |
[
{
"content": "Evaluate the limit: \\[ \\lim_{(x,y) \\to (0,0)} \\frac{e^{x+y}-(x+y+1)}{\\sqrt{x^2 +y^2}}. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether both $p^{\\frac{r}{q}}$ and $q^{\\frac{r}{p}}$ can be rational numbers if $p$, $q$, and $r$ are distinct prime numbers.",
"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... | 1.306 |
[
{
"content": "Let $W$ be the finite $\\mathbb{Z}$-module obtained from $\\mathbb{Z}_q^n$ with addition componentwise. Let $V$ be a submodule of $W$. Define $V^{\\perp} = \\{w \\in W \\mid \\forall v \\in V, \\; v \\cdot w = 0 \\}$ where \"\\cdot\" denotes the dot product. Determine whether ${(V^{\\perp})}^{\\pe... | (V^{\perp})^{\perp} = V |
[
{
"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... | $48,000 |
[
{
"content": "Evaluate the limit: \\[ \\lim _{x\\to -\\infty }\\frac{3x^7-25x^5+e^{-\\frac{x^3}{(1-x)^3}}}{-5x^7+111! \\cdot x} \\]",
"role": "user"
}
] | -\dfrac{3}{5} |
[
{
"content": "Does there exist an infinite-dimensional Hilbert space $X$ such that every convergent sequence in $X$ is relatively compact?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_{|z|=1} \\frac{\\sin(z^2)}{(\\sin(z))^2} \\, dz \\) where \\( z \\in \\mathbb{C} \\).",
"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... | [Xe]4f^{14}5d^{3}6s^{0} |
[
{
"content": "Find all functions \\( f: \\mathbb{N}_0 \\rightarrow \\mathbb{N}_0 \\) such that \\( f(f(n)) + f(n) = 2n + 6 \\) for all \\( n \\in \\mathbb{N}_0 \\).",
"role": "user"
}
] | f(n) = n + 2 |
[
{
"content": "Determine the area of the region bounded by the polar curve \\( r = 3\\sin(2\\theta) \\) for \\( \\theta \\in [0, \\pi/2] \\) using Green's Theorem.",
"role": "user"
}
] | \dfrac{9\pi}{8} |
[
{
"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... | CARDINAL TRAITS |
[
{
"content": "Determine whether the following statement is true or false: If $\\Omega\\subset\\mathbb{R}^n$ is bounded and $u,v\\in W^{1,\\,p}(\\Omega)\\cap L^\\infty(\\Omega)$, then $uv\\in W^{1,\\,p}(\\Omega)\\cap L^\\infty(\\Omega)$ and $$\\nabla(uv)=u\\nabla v+v\\nabla u.$$",
"role": "user"
}
] | True |
[
{
"content": "A rectangular parallelepiped has dimensions such that \\( AB = 4 \\), \\( AD = AA_1 = 14 \\). Point \\( M \\) is the midpoint of edge \\( CC_1 \\). Calculate the area of the section of the parallelepiped created by the plane passing through points \\( A_1, D, \\) and \\( M \\).",
"role": "user... | \dfrac{189}{2} |
[
{
"content": "Let $G$ be a finite abelian group and $G^{(p)}$ its unique $p$-Sylow subgroup. Determine if there exists a subgroup $H \\subseteq G$ such that $G/H \\cong G^{(p)}$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\rightarrow -\\infty}\\frac{\\int_{x}^{0} \\sin(t^{3})dt}{\\int_{x^{2}}^{0}\\frac{\\cos(t)}{t^{3}} dt}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Consider the function \\( f(x) \\) defined as follows: \\( f(x) = \\begin{cases} x^2 + 1, & \\text{if } x \\text{ is irrational} \\\\ \\tan(x), & \\text{if } x \\text{ is rational} \\end{cases} \\) in the interval \\([0, 4\\pi]\\). Determine the number of points \\( x \\) within this interval wher... | 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... | 0.234 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... | -3.4e7 N/C |
[
{
"content": "Evaluate the sum \\( \\sum_{n=0}^{\\infty} \\frac{2n}{8^n}{{2n}\\choose{n}} \\).",
"role": "user"
}
] | \sqrt{2} |
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