prompt list | ground_truth string |
|---|---|
[
{
"content": "Given an infinitely differentiable function \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f(0) = 0 \\), \\( f(x) > 0 \\) for all \\( x \\neq 0 \\), and \\( f^{(n)}(0) = 0 \\) for all \\( n \\in \\mathbb{N} \\), determine if the function \\( g(x) := \\sqrt{f(x)} \\) is infinitely differenti... | 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... | Forward rate premium (p) = Forward rate (FR) - Spot rate (S) |
[
{
"content": "Evaluate the limit \\( \\lim_{x \\rightarrow 0^+}(e^{\\frac{1}{x}}x^2) \\) without using L'Hopital's rule.",
"role": "user"
}
] | \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... | -31.97% |
[
{
"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... | 100,000 units |
[
{
"content": "Find the value of \\(a \\in \\mathbb{R}\\) such that the sequence \\(x_n = \\frac{1}{3} \\cdot \\frac{4}{6} \\cdots \\frac{3n-2}{3n} n^a\\) converges to a positive real number.",
"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... | 106,200 |
[
{
"content": "If the three lines $3y-2x=1$, $x+2y=2$ and $4x-6y=5$ are drawn in the plane, how many points will lie at the intersection of at least two of the three lines?",
"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... | General Journal
Debit Credit
Work-in Process $510,814
Labor rate Variance $39,720
Labor Efficiency Variance $26,230
Wages Payable (39,720 hours * $11.20) $444,864 |
[
{
"content": "Let $p > 2$ be a prime number. Determine the order of the group $G$ of invertible $2 \\times 2$ matrices over $\\mathbb{Z}_p$ whose determinant is $-1$. It is known that $G \\leq GL_2(\\mathbb{Z}_p)$ and $|GL_2(\\mathbb{Z}_p)| = p(p^2 - 1)(p - 1)$. Find the order of $G$. \\( \\boxed{\\text{Order o... | p(p^2 - 1) |
[
{
"content": "Evaluate the integral expression: $$\\int^1_0 \\frac{1}{(1+x^{2015})(1+x^2)}\\,dx + \\int^1_0 \\frac{y^{2015}}{(1+y^{2015})(1+y^2)}\\,dy$$",
"role": "user"
}
] | \dfrac{\pi}{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... | 40.6 % |
[
{
"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... | 4.327 m |
[
{
"content": "Let $f: \\mathbb{R} \\to \\mathbb{R}$ be a function such that $\\int_{-\\infty}^{\\infty} |f(z)| \\, dz < \\infty$. Determine whether $\\lim_{h \\to \\infty} \\int_{|f(z)| > h} f(z) \\, dz = 0$. Justify your answer.",
"role": "user"
}
] | 0 |
[
{
"content": "Let $c=2^{\\aleph_0}$, $x=2^c$, $y=2^{2^c}$, and $z=2^{2^{2^c}}$. Arrange the expressions $x^{y^z}$, $x^{z^y}$, and $y^{z^x}$ in ascending order.",
"role": "user"
}
] | x^{z^y} = y^{z^x} < x^{y^z} |
[
{
"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... | 3.99e-3 m/s^2 |
[
{
"content": "Find the arc length of the curve defined by the parametric equations \\(x(t) = t\\sin(2t)\\), \\(y(t) = t\\cos(2t)\\), and \\(z(t) = \\frac{4}{3}t\\sqrt{t}\\) from \\(t=0\\) to \\(t=2\\pi\\).",
"role": "user"
}
] | 4\pi^2 + 2\pi |
[
{
"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... | 228/232 |
[
{
"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... | 288 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... | 68685 |
[
{
"content": "Let \\( f \\) be a homomorphism from the real numbers under addition to the nonzero complex numbers under multiplication. Determine the image of \\( f \\).",
"role": "user"
}
] | \{ e^{zt} \mid t \in \mathbb{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... | knowledge |
[
{
"content": "Let $S$ be a subspace of a topological space $X$, and let $E$ be a subset of $S$. Prove that the relative closure of $E$ in $S$ is $E^* \\cap S$, where $E^*$ is the closure of $E$ in $X$. ",
"role": "user"
}
] | E^* \cap 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... | 482 |
[
{
"content": "In graph theory, determine whether any maximal star in a graph $G$ is necessarily a bond. Provide a true or false answer.",
"role": "user"
}
] | False |
[
{
"content": "Find the length of the curve formed by the intersection of the unit sphere \\(x^2 + y^2 + z^2 = 1\\) and the plane \\(x + y = 1\\).",
"role": "user"
}
] | \pi \sqrt{2} |
[
{
"content": "Suppose $X$ is an exponential random variable with mean 10 and $Y$ is a Bernoulli random variable with success probability 0.6. Assume $X$ and $Y$ are independent. Calculate the variance of the product $XY$, denoted as $\\operatorname{Var}[XY]$. \\( \\boxed{?} \\)",
"role": "user"
}
] | 84 |
[
{
"content": "Two curves are given by the equations \\( y=2 \\sin \\frac{5 \\pi}{6}x \\) and \\( y=\\alpha x^2-3 \\alpha x+2\\alpha +1 \\). If these curves touch each other at some point within the interval \\( 0 \\leq x \\leq \\frac{18}{5} \\), find the value of \\( \\frac{2 \\sqrt{3} \\alpha}{5 \\pi} \\).",
... | 1 |
[
{
"content": "Given positive numbers $a, b, c$ that satisfy the equation $a^{2}b + b^{2}c + c^{2}a = 3$, find the minimum value of the expression:\n\n$$\nA = a^{7}b + b^{7}c + c^{7}a + ab^{3} + bc^{3} + ca^{3}.\n$$",
"role": "user"
}
] | 6 |
[
{
"content": "Let \\( x = -\\sqrt{2} + \\sqrt{3} + \\sqrt{5} \\), \\( y = \\sqrt{2} - \\sqrt{3} + \\sqrt{5} \\), and \\( z = \\sqrt{2} + \\sqrt{3} - \\sqrt{5} \\). Evaluate the expression:\n$$\n\\frac{x^{4}}{(x-y)(x-z)} + \\frac{y^{4}}{(y-z)(y-x)} + \\frac{z^{4}}{(z-x)(z-y)}\n$$",
"role": "user"
}
] | 20 |
[
{
"content": "Calculate \\( \\lim_{x\\to 0^+} \\frac{x^x- (\\sin x)^x}{x^3} \\).",
"role": "user"
}
] | \dfrac{1}{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... | s(t) = \frac{t^4}{12}+\frac{2t^3}{3}+3t^2+19.58t |
[
{
"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... | 1.20 N |
[
{
"content": "Let $G$ be a group and let $H$ and $N$ be subgroups of $G$. Suppose that $[G:H] \\leq |N|$. Does this always imply that $[G:N] \\leq |H|$? Determine whether this statement is true in general, not just in the finite case.",
"role": "user"
}
] | True |
[
{
"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... | 3.04*10^-1 H atoms |
[
{
"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... | 0.0118 J |
[
{
"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... | (4.1n*10^-3+3.7)*10^-4 T |
[
{
"content": "Let $p(x)$ be a polynomial of degree four with extrema at $x=1$ and $x=2$. Given that \\( \\lim \\limits_{x \\to 0}\\left(1+\\frac{p(x)}{x^2}\\right)=2 \\), find the value of $p(2)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "In how many ways can the letters of the word \"INDIVISIBILITY\" be rearranged such that no two 'I's are adjacent?",
"role": "user"
}
] | 3386880 |
[
{
"content": "Find the probability that for four independent random variables \\(x_1, x_2, x_3, x_4\\) uniformly distributed over the interval \\([0, a]\\), the inequality \\(x_1 > x_2 + x_3 + x_4\\) holds.",
"role": "user"
}
] | \dfrac{1}{24} |
[
{
"content": "For a differential operator $P$ of order $p$ and a multi-index $\\beta$, determine the maximum possible order of the commutator $[P, \\partial_x^\\beta]$. Provide your answer as an expression in terms of $p$ and $|\\beta|$.",
"role": "user"
}
] | p + |\beta| - 1 |
[
{
"content": "In parallelogram \\(ABCD\\), \\(\\angle B = 111^\\circ\\) and \\(BC = BD\\). A point \\(H\\) is on segment \\(BC\\) such that \\(\\angle BHD = 90^\\circ\\). Let \\(M\\) be the midpoint of \\(AB\\). Determine the measure of angle \\(AMH\\) in degrees.",
"role": "user"
}
] | 132 |
[
{
"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... | 0.84 cm |
[
{
"content": "Find the smallest positive integer value of $f$ such that there exist distinct positive integers $a, b, c, d, e$ satisfying the equation $a^2 + b^2 + c^2 + d^2 + e^2 = f^2$. What is this value of $f$?",
"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... | $39,000.00 |
[
{
"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... | 24.64 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... | 1.896 |
[
{
"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... | 25.2 Wb |
[
{
"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... | 51.4 m/s^2 |
[
{
"content": "There are four points that are $5$ units from the line $y=13$ and $13$ units from the point $(7,13)$. What is the sum of the $x$- and $y$-coordinates of all four of these points?",
"role": "user"
}
] | 80 |
[
{
"content": "Determine the time complexity of finding the most significant digit of the number $3\\uparrow\\uparrow n$, where $3\\uparrow\\uparrow n$ represents a power tower of 3s of height $n$.",
"role": "user"
}
] | O(n) |
[
{
"content": "Determine the rank of the symmetric matrix $X^TDX$, where $X$ is a real $(n \\times p)$ matrix and $D$ is a diagonal $(n \\times n)$ matrix with all diagonal entries $d_{ii} > 0$. Provide your answer in terms of $n$ and $p$.",
"role": "user"
}
] | \min(n, p) |
[
{
"content": "How many pairs of natural numbers \\((x, y)\\), where both are not greater than 100, satisfy the conditions that the difference \\(x - y\\) is a prime number and the product \\(xy\\) is a perfect square?",
"role": "user"
}
] | 7 |
[
{
"content": "Determine if $f(x) = C \\log x$ $(C \\in \\mathbb{R})$ is the only solution to the equation $\\sum_{i=1}^{n} f(x_{i}) = f(\\prod_{i=1}^{n} x_{i})$ for $x_{i} \\in \\mathbb{R}_{+}^{*}$. Provide a justification for your answer.",
"role": "user"
}
] | f(x) = C \log x |
[
{
"content": "Let $a_1 = 1$ and $a_{n+1} = a_n \\cdot p_n$ for $n \\geq 1$, where $p_n$ is the $n$th prime number, starting with $p_1 = 2$. Let $\\tau(x)$ be the number of divisors of $x$. Find the remainder when \\( \\sum_{n=1}^{2020} \\sum_{d \\mid a_n} \\tau (d) \\) is divided by 91, where $d$ is a positive ... | 40 |
[
{
"content": "Find all 4-digit numbers \\( n \\) such that \\( n = pqr \\), where \\( p < q < r \\) are distinct primes, \\( p + q = r - q \\), and \\( p + q + r = s^2 \\), where \\( s \\) is a prime number.",
"role": "user"
}
] | 2015 |
[
{
"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... | 1.142e5 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... | $161,613 |
[
{
"content": "Calculate the flux of the vector field \\( F(x,y,z) = \\left(\\frac{1}{6}x^2yz,\\frac{1}{4}xy^2z,\\frac{1}{12}xyz^2\\right) \\) through the surface \\( \\Omega = \\{(x,y,z) \\in \\mathbb{R}^3 : 0 \\leq x,y,z \\leq 2\\} \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Let \\( V \\) and \\( W \\) be finite-dimensional vector spaces over an infinite field \\( k \\). Fix a positive integer \\( n \\leq \\min(\\dim(W), \\dim(V)) \\). Given \\( n \\) injective linear maps \\( f_i:V\\rightarrow W \\), such that the \\( f_i \\) are linearly independent as elements of \... | 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... | 409 |
[
{
"content": "Find the residue of the function \\( f(z) = (z^2 + 4iz)\\sin\\left(\\frac{3}{z + 2i}\\right) \\) at \\( z_0 = -2i \\) using the Laurent series expansion.",
"role": "user"
}
] | \dfrac{15}{2} |
[
{
"content": "Find the limit of \\((\\tanh x)^{2x}\\) as \\(x\\) approaches infinity using L'Hopital's rule.",
"role": "user"
}
] | 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... | Current Liabilities:
Notes Payable: $25,000
Interest Payable: $120 (Short-term notes payable) + $750 (Long-term notes payable) = $870
Warranty Liability: $540
Accounts Payable: $16,000
Salaries Payable: $1,400
Vacation Pay: $2,160
Total Current Liabilities: $45,970 |
[
{
"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... | -$3,000 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\int_0^{\\frac{1}{2^n}}(1+\\cos(x))^n\\, dx \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0}\\frac{\\pi\\sin{x}-\\sin{\\pi x}}{x(\\cos{x}-\\cos(\\pi x))}$$",
"role": "user"
}
] | \dfrac{\pi}{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... | $910.33 |
[
{
"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... | transfection |
[
{
"content": "Solve for $e$, given that $2d$ is $8$ less than $17e$, and $2e$ is $9$ less than $d$.",
"role": "user"
}
] | 2 |
[
{
"content": "Let \\( f: (-1, +\\infty) \\to (-1, +\\infty) \\) be a continuous and monotonic function with \\( f(0) = 0 \\) and satisfying the inequality\n\\[ f[x + f(y) + x f(y)] \\geqslant y + f(x) + y f(x) \\quad \\text{for all} \\quad x, y \\in (-1, +\\infty). \\]\nDetermine the function \\( f(x) \\).",
... | f(x) = x |
[
{
"content": "Determine all values of the parameter \\(a\\) for which the inequality \\(3 - |x-a| > x^2\\) is satisfied by at least one negative \\(x\\).",
"role": "user"
}
] | \left( -\frac{13}{4}, 3 \right) |
[
{
"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... | Contributed Capital: Beginning balance $104,000, Issued Stock $35,000, Ending Balance $139,000. Retained Earnings: Beginning balance $54,000, Net Income $59,000, Dividend Paid $(21,000), Ending Balance $92,000 |
[
{
"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... | 5.5% |
[
{
"content": "Find the explicit Cartesian equation for the surface obtained by revolving the curve \\( y = \\frac{1}{x} \\) about the line \\( y = x \\).",
"role": "user"
}
] | 2xy - z^2 = 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... | 40.64 m |
[
{
"content": "Determine the interval of convergence for the power series \\( \\sum_{n=0}^{\\infty} \\frac{(2x-3)^n}{n \\ \\ln n} \\).",
"role": "user"
}
] | [1, 2) |
[
{
"content": "Is it necessary for the matrices $A$, $B$, and $C$ to be positive definite for the block matrix \\( Y = \\begin{bmatrix} A & F & G \\\\ F' & B & E \\\\ G' & E' & C \\end{bmatrix} \\) to be positive definite?",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the signed curvature of the unit-speed reparametrization of the curve \\( h(u) = (\\cos^2(u), \\sin^2(u)) \\) starting at \\( u = 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... | $317,586.75 |
[
{
"content": "Consider the function \\( f(x,y) = \\frac{xy^2}{x^2+y^4} \\) for \\( x \\neq 0 \\) and \\( f(x,y) = 0 \\) for \\( x = 0 \\). Determine which of the following statements is true about the function at the origin:\n\n1. It is continuous but not differentiable at the origin.\n2. It is differentiable a... | 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... | 435000 |
[
{
"content": "Find the sum of the infinite series: \\[ 1 + \\frac{1}{1!} \\cdot \\frac{1}{4} + \\frac{1 \\cdot 3}{2!} \\cdot \\left(\\frac{1}{4}\\right)^2 + \\frac{1 \\cdot 3 \\cdot 5}{3!} \\cdot \\left(\\frac{1}{4}\\right)^3 + \\cdots \\] where the dot represents multiplication and the exclamation mark denotes... | \sqrt{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... | 7.259 * 10^-4 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... | -2.88e-9 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... | 10 days |
[
{
"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... | -100,000 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\frac{\\sum_{k=1}^n \\frac{n-k+1}{k}}{\\ln(n!)} \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Let \\( f \\) be a function such that \\( \\lim_{h \\to 0} \\frac{f(x+h) - f(x-h)}{2h} = 0 \\) for all real numbers \\( x \\). Does this imply that \\( f \\) is continuous? 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... | 1.05e-6 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... | $9,364.58 |
[
{
"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... | [BrF] = 0.710 M, [Br_2] = [F_2] = 0.095 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... | 3.17e-10 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... | $8,989 |
[
{
"content": "Given two linear functions \\( f(x) \\) and \\( g(x) \\) such that the graphs \\( y=f(x) \\) and \\( y=g(x) \\) are parallel lines, but not parallel to the coordinate axes, find the minimum value of the function \\( (g(x))^2 - 3f(x) \\), if the minimum value of the function \\( (f(x))^2 - 3g(x) \\... | -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... | 5.0 mol |
[
{
"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 = 37.4 cm and x = -36.5 cm |
[
{
"content": "Determine the minimum number of equations required to ensure that an $n \\times n$ matrix has a rank of at most $n-3$. Provide your answer as a single integer.",
"role": "user"
}
] | 9 |
[
{
"content": "Calculate an upper bound for the norm of the linear functional \\( \\phi_n: (C[0,1], \\Vert{\\cdot}\\Vert_\\infty) \\to \\mathbb{R} \\) defined by \\( \\phi_n(x) = \\int_0^1 t^n x(t) \\, dt \\), which is independent of \\( n \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find the distance between the foci of the hyperbola\n\\[\\frac{y^2}{18} - \\frac{x^2}{2} = 1.\\]",
"role": "user"
}
] | 4 \sqrt{5} |
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