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... | $2,400 |
[
{
"content": "Let $f: \\mathbb{R}^a \\to \\mathbb{R}^b$ and $g: \\mathbb{R}^c \\to \\mathbb{R}^d$ be $C^\\infty$ functions. Define the Cartesian product of these functions as $(f \\times g)(x, y) = (f(x), g(y))$. Is the function $f \\times g$ also $C^\\infty$?",
"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... | $4.19 |
[
{
"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... | 39.2m |
[
{
"content": "What is the value of $a$ if the lines $2y - 2a = 6x$ and $y + 1 = (a + 6)x$ are parallel?",
"role": "user"
}
] | -3 |
[
{
"content": "Find the length of the curve defined by the equations $z^2 = 2x$ and $3y = xz$ between the points $(0,0,0)$ and $(\\frac{1}{2},\\frac{1}{6},1)$. Express the curve parametrically as $\\vec{r}(t) = (x(t), y(t), z(t))$ and compute the arc length integral.",
"role": "user"
}
] | \dfrac{7}{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... | 31 mL |
[
{
"content": "Is the algebraic Grothendieck group of a weighted projective space finitely generated?",
"role": "user"
}
] | Yes |
[
{
"content": "Suppose we roll a fair 6-sided die repeatedly. What is the expected number of rolls required to see 3 of the same number in succession?",
"role": "user"
}
] | 43 |
[
{
"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... | 2.17 g |
[
{
"content": "Determine if the projection operator $P: W \\rightarrow W$ on a subspace $W$ of a real vector space $V$ is diagonalizable.",
"role": "user"
}
] | Yes |
[
{
"content": "Suppose that $f$ and $g$ are positive and continuous functions on $[1,\\infty)$. If $\\lim_{x\\to\\infty} \\frac{f(x)}{g(x)} = 0$, does it follow that $\\lim_{x\\to\\infty} \\frac{\\int_x^\\infty f}{\\int_x^\\infty g} = 0$? Provide a justification for your answer.",
"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... | 3e-6 T |
[
{
"content": "Equilateral $\\triangle ABC$ has side length $600$. Points $P$ and $Q$ lie outside the plane of $\\triangle ABC$ and are on opposite sides of the plane. Furthermore, $PA=PB=PC$, and $QA=QB=QC$, and the planes of $\\triangle PAB$ and $\\triangle QAB$ form a $120^{\\circ}$ dihedral angle (the angle ... | 450 |
[
{
"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... | 44.1 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... | Corporate citizenship |
[
{
"content": "Given the sequence defined by \\( x_1 = 5, x_2 = 401 \\), and \\( x_n = x_{n-2} - \\frac{1}{x_{n-1}} \\) for every \\( 3 \\leq n \\leq m \\), determine the largest possible value of \\( m \\). \n\n\\( \\textbf{(A)}\\ 406 \\qquad\\textbf{(B)}\\ 2005 \\qquad\\textbf{(C)}\\ 2006 \\qquad\\textbf{(D)}\... | 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... | 12.59% |
[
{
"content": "Let $M$ be a subspace of $\\mathbb{R}^4$ defined by the equations $x + y - z = 0$ and $t = x + y$. Find a basis for $M^T \\cap M$ and determine its dimension.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following claim is true or false: Let $\\mu$ be a Borel probability measure with compact support on $\\mathbb{R}$. The measure $\\mu$ is not a Dirac measure if and only if $|\\hat{\\mu}(\\xi)|\\not\\equiv1$ for $\\xi\\in \\mathbb{R}$. Justify your answer.",
"role": "user"... | True |
[
{
"content": "Given that $M = Gab^2c^3d^4$ where $a, b, c, d$ are distinct prime numbers, calculate the probability that a pair of numbers randomly chosen from the set of numbers of the form $Ga^ib^jc^kd^l$ (where $0 \\leq i \\leq 1$, $0 \\leq j \\leq 2$, $0 \\leq k \\leq 3$, $0 \\leq l \\leq 4$) will have a gr... | \dfrac{2}{1785} |
[
{
"content": "Let $f: \\mathbb{R} \\to \\mathbb{R}$ be a differentiable function such that $f(3) = 3$ and $f'(3) = \\frac{1}{2}$. Evaluate the limit: \\[ \\lim_{x \\to 3} \\int_{3}^{f(x)} \\frac{2t^3}{x-3} \\, dt. \\]",
"role": "user"
}
] | 27 |
[
{
"content": "Simplify the ordinal expression \\((\\omega + 1) + \\omega\\).",
"role": "user"
}
] | \omega \cdot 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... | x_CH2Cl2 = 0.375, x_CH2Br2 = 0.625 |
[
{
"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-methylpentane |
[
{
"content": "Let \\( Z \\sim G(p) \\) and \\( W \\sim G(2p) \\) be independent random variables. Given that \\( P(W > Z - 1) = \\frac{3}{7} \\), calculate the value of \\( p \\).",
"role": "user"
}
] | \dfrac{1}{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... | 4.2e-19 J |
[
{
"content": "Let $f: \\mathbb{R} \\to \\mathbb{R}$ be a non-constant function such that for any metric $d$ on $\\mathbb{R}$, $f: (\\mathbb{R}, d) \\to (\\mathbb{R}, d)$ is continuous. Determine if $f$ must be the identity function, i.e., $f(x) = x$ for all $x \\in \\mathbb{R}$. Provide a proof or counterexampl... | f(x) = x |
[
{
"content": "Let $a_2$, $a_1$, and $a_0$ be three digits. When the 3-digit number $a_2 a_1 a_0$ is read in base $b$ and converted to decimal, the result is 254. When the 3-digit number $a_2 a_1 a_0$ is read in base $b + 1$ and converted to decimal, the result is 330. Finally, when the 3-digit number $a_2 a_1 a... | 512 |
[
{
"content": "Calculate the remainder when \\((4^{103} + 2 \\times 5^{104})^{102}\\) is divided by 13.",
"role": "user"
}
] | 12 |
[
{
"content": "Four diagonals of a regular octagon with side length 2 intersect as shown. Find the area of the shaded region. [asy]\npair A, B, C, D, E, F, G, H;\nreal x = 22.5;\npair A = dir(x);\npair B = dir(45+x);\npair C = dir(45*2+x);\npair D = dir(45*3+x);\npair E = dir(45*4+x);\npair F = dir(45*5+x);\npa... | 4\sqrt{2} |
[
{
"content": "Determine the number of homomorphisms from the dihedral group $D_{21}$ to the dihedral group $D_{15}$. Provide your answer as a single integer.",
"role": "user"
}
] | 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... | 3.77 years |
[
{
"content": "Evaluate the infinite series \\( \\sum_{k=1}^{\\infty}\\frac{18[(k-1)!]^2}{(2k)!} \\).",
"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... | sqrt(6) 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... | 0.094 m |
[
{
"content": "Determine whether the series \\( \\sum_{n=1}^{\\infty}\\left(\\cos\\frac{1}{n}\\right)^{k(n)} \\) converges, where \\( k(n)=\\frac{1}{\\sin^a\\left(\\frac{1}{n}\\right)} \\) and \\( a \\in \\mathbb{R} \\). Use the approximations \\( \\cos\\frac{1}{n} \\approx 1-\\frac{1}{2n^2} \\) and \\( \\sin^a\... | a > 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... | 2.9 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... | 12.28 g |
[
{
"content": "In a perfect graph, does there exist a clique that intersects all maximal independent sets?",
"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... | 729\pi / 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... | 12:1 |
[
{
"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... | 2.385 mm |
[
{
"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... | 12.95 hours |
[
{
"content": "Let \\( f(x) \\) be an odd function defined on \\( \\mathbf{R} \\), with \\( f(1)=2 \\). When \\( x>0 \\), \\( f(x) \\) is an increasing function. Additionally, for any \\( x, y \\in \\mathbf{R} \\), \\( f(x+y)=f(x)+f(y) \\). Determine the maximum value of \\( f(x) \\) on the interval \\([-3, -2]\... | -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... | 81.22 m/s |
[
{
"content": "Determine the values of \\( \\alpha \\) for which the series \\( \\sum_{n=1}^{\\infty} \\frac{n^2+n-1}{\\sqrt{n^\\alpha+n+3}} \\) converges.",
"role": "user"
}
] | \alpha > 6 |
[
{
"content": "Find the supremum of the expression \\( \\frac{ |x + 2y| + 2|y|}{|x| + |y|} \\) for \\(x, y \\in \\mathbb{R}\\).",
"role": "user"
}
] | 4 |
[
{
"content": "Let \\(a\\) be a root of the polynomial \\(x^3 + x^2 + 1\\) in some extension of the field \\(\\mathbb{Z}_2\\). Determine the multiplicative inverse of \\(a+1\\) in this extension.",
"role": "user"
}
] | a^2 |
[
{
"content": "Determine the coefficient of $z$ in the Laurent series expansion of \\( \\frac{e^z}{z-1} \\) for the region \\( \\{|z|>1\\} \\).",
"role": "user"
}
] | e - 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... | 80.0 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... | 20.4 m |
[
{
"content": "Determine whether there exists a real number $x$ such that its irrationality measure $\\mu(x)$ equals $\\lambda$ for any given $\\lambda \\in [2, +\\infty)$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the order of accuracy of the finite difference expression \\( \\frac{(a_{i+1} + a_i)(u_{i+1} - u_i) - (a_i + a_{i-1})(u_i - u_{i-1})}{2h^2} \\) as an approximation to \\( \\frac{d}{dx}\\Big(a(x) \\frac{du}{dx} \\Big)\\bigg|_{x_i} \\), where \\( h \\) is the mesh width, and \\( a_i = a(x_... | 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... | 0.24 T |
[
{
"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... | 8.33 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... | 1.482e8 m/s |
[
{
"content": "In triangle \\( PQR \\), the median \\( PA \\) and the angle bisector \\( QB \\) intersect at point \\( O \\). Given that \\( 3PQ = 5QR \\), find the ratio of the area of triangle \\( PQR \\) to the area of triangle \\( PQO \\).",
"role": "user"
}
] | \dfrac{13}{5} |
[
{
"content": "If $X$ and $Y$ are independent, continuous random variables with the same probability density function, determine whether $P(X > Y) = \\frac{1}{2}$ is true.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find the norm of the functional defined on $l_1$ by $$ x=(x_n) \\mapsto \\sum \\frac{x_n-x_{n+1}}{3^n}. $$",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Find all functions \\( f : \\mathbb{R}^+ \\to \\mathbb{R}^+ \\) satisfying the equation \\[ \\frac{f(f(y)^2 + xy)}{f(y)} = f(x) + y \\] for all \\( x, y \\in \\mathbb{R}^+ \\).",
"role": "user"
}
] | f(x) = x |
[
{
"content": "Determine the denominator of the coefficient of the integral of the polynomial \\((x-\\alpha)^5(x-\\beta)^4\\) with respect to \\(x\\), given that \\(\\beta > \\alpha\\).",
"role": "user"
}
] | 2520 |
[
{
"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... | 661.76 kPa |
[
{
"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... | 146 K |
[
{
"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... | Firm B has a greater return on equity (11.69%) than Firm A (10.64%). |
[
{
"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... | 724g Na2O |
[
{
"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... | 8.21e-4 J |
[
{
"content": "Determine the number of ways to arrange red balls in 6 places such that in any 3 consecutive places, there are at least 2 red balls. Use the minimum number of red balls possible.",
"role": "user"
}
] | 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... | -$254M |
[
{
"content": "Let \\( f: \\mathbb{Z}_{>0} \\rightarrow \\mathbb{Z} \\) be a function with the following properties:\n\n1. \\( f(1)=0 \\),\n2. \\( f(p)=1 \\) for all prime numbers \\( p \\),\n3. \\( f(xy)=y f(x)+x f(y) \\) for all \\( x, y \\in \\mathbb{Z}_{>0} \\).\n\nDetermine the smallest integer \\( n \\geq ... | 3125 |
[
{
"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... | 16.02 m |
[
{
"content": "For which integer values of \\( n \\ge 2 \\) can the real numbers \\( x_1, x_2, \\ldots, x_n \\) be uniquely determined from the sums \\( x_i + x_j \\) for all \\( 1 \\le i < j \\le n \\)?",
"role": "user"
}
] | n \geq 3 |
[
{
"content": "What is the value of $x$ in the diagram?\n\n[asy]\nimport olympiad;\ndraw((0,0)--(sqrt(3),0)--(0,sqrt(3))--cycle);\ndraw((0,0)--(-1,0)--(0,sqrt(3))--cycle);\nlabel(\"2\",(-1/2,sqrt(3)/2),NW);\nlabel(\"$x$\",(sqrt(3)/2,sqrt(3)/2),NE);\ndraw(\"$45^{\\circ}$\",(1.5,0),NW);\ndraw(\"$60^{\\circ}$\",(-0... | \sqrt{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... | 7r/12 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} \\left( (x+3)^{1 + \\frac{1}{x}} - x^{1 + \\frac{1}{x+3}} \\right) \\]",
"role": "user"
}
] | 3 |
[
{
"content": "Given that \\( x, y, z \\) are positive numbers and \\( x^{2} + y^{2} + z^{2} = 1 \\), find the minimum value of:\n\\[ S = \\frac{xy}{z} + \\frac{yz}{x} + \\frac{zx}{y}. \\]",
"role": "user"
}
] | \sqrt{3} |
[
{
"content": "Given that $a, b \\in \\mathbb{R}$ and $a \\neq 0$, when the polynomial $x^2 - 2ax + a^4$ is divided by $x + b$, the remainder is 1. Additionally, the polynomial $bx^2 + x + 1$ has $ax - 1$ as a factor. Determine the value of $b$. \\( \\text{(Express your answer as a real number.)} \\)",
"role... | -2 |
[
{
"content": "Is it possible to label $n$ points in the unit square such that the sum of the squares of the distances between consecutive points and the first point exceeds 10?",
"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... | 7.50e-11 m/s^2 |
[
{
"content": "Given ordered sets $X$ and $Y$, construct the set $Z = X \\times Y$ with cardinalities $|X| = m$, $|Y| = n$, and $|Z| = m \\times n$. There are $3^{m \\times n}$ different three-way partitions of $Z$, denoted as $P(Z)$. Define a new partition strategy $Q(Z)$, which partitions $Z$ based on $X$ firs... | 3^{m + n + 1} |
[
{
"content": "Let the ellipse be defined by \\(\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1\\) and let \\(AB\\) be a chord of the ellipse. The elliptical angle of point \\(A\\) is \\(\\alpha\\) and the elliptical angle of point \\(B\\) is \\(\\beta\\). The chord \\(AB\\) intersects the major axis at point \\(C\\), and t... | 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... | sp3 |
[
{
"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... | zero |
[
{
"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_3=f/y_1*x_1 |
[
{
"content": "Find the smallest positive integer \\(x\\) such that \\(2^x \\equiv 43 \\pmod{59}\\).",
"role": "user"
}
] | 33 |
[
{
"content": "Evaluate the integral: $$\\int_{-\\infty}^\\infty x^2e^{-|x|}\\ dx$$",
"role": "user"
}
] | 4 |
[
{
"content": "Determine the values of $z$ for which the function $g(z) = \\cos(x)\\cosh(y) + i\\sin(x)\\sinh(y)$ is differentiable.",
"role": "user"
}
] | z = n\pi |
[
{
"content": "Let \\(g(x)=mx^2+nx+p\\) be a quadratic function with \\(m, n, p \\in \\mathbb{R}\\) such that \\(|g(x)|\\leq 2\\) for \\(|x|\\leq 2\\). Determine the maximum possible value of \\(|g'(x)|\\) on the interval \\(|x|\\leq 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... | 2.19e-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... | 1.33 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... | -11454.20 kJ/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... | 157 kPa |
[
{
"content": "Determine whether there exists a pair of consecutive positive integers, both of which are super exponential numbers. A number is super exponential if its prime factorization includes at least one prime raised to the power of 1000 or higher.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine if the function \\( u(x,y) = \\frac{x}{x^2+y^2} \\) is harmonic away from the origin by using its polar coordinate representation.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the limit of the sequence as \\( n \\to \\infty \\): $$\\left(\\frac{\\ln 2}{2}+\\frac{\\ln 3}{3}+\\cdots + \\frac{\\ln n}{n} \\right)^{\\frac{1}{n}}$$",
"role": "user"
}
] | 1 |
[
{
"content": "Provide an example of a linear operator \\( T \\) acting on an infinite-dimensional complex vector space \\( X \\) such that \\( T \\) does not possess any eigenvalues.",
"role": "user"
}
] | T |
[
{
"content": "Determine the radius of convergence for the power series \\( \\sum_{n=0}^{\\infty} (-1)^{n} (\\sqrt[n]{n})^n x^n \\).",
"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... | 0.35 A |
[
{
"content": "Evaluate the contour integral \\( \\oint_C |z|^2 \\, dz \\) for the square contour \\( C \\) with vertices at \\((0,0), (1,0), (1,1),\\) and \\((0,1)\\).",
"role": "user"
}
] | -1 + i |
[
{
"content": "Find the limit of \\( P\\left(Y_n \\geq \\frac{n}{2} - n^{2/3} \\right) \\) as \\( n \\to \\infty \\), where \\( Y_n \\) is the sum of \\( n \\) i.i.d. random variables each uniformly distributed over \\( (0, 1) \\).",
"role": "user"
}
] | 1 |
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