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... | 1512.3 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... | 0.0016N |
[
{
"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... | $20.94 |
[
{
"content": "Consider an infinite-dimensional vector space $V$ consisting of polynomials over the real numbers $\\mathbb{R}$. Let $W$ be a subspace of $V$ that contains all polynomials divisible by $x^4$. Determine the dimension of the quotient space $V/W$. \\( \\text{Provide your answer as a single integer.} ... | 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... | 309.11 kg |
[
{
"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... | 4.32e5 Pa |
[
{
"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... | 4888.38 |
[
{
"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... | 147N |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty} dx \\, dy \\, \\exp(-5x^2+8xy-5y^2) \\) using techniques such as completing the square and making suitable substitutions.",
"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... | 373 kN |
[
{
"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... | 6.54e-7 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... | -$365,310 |
[
{
"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... | $1,816,000 |
[
{
"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... | $2,770.62 |
[
{
"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... | $6.44 |
[
{
"content": "Evaluate the complex integral \\(\\int_{1-i\\infty}^{1+i\\infty} \\frac{1}{t^2} \\mathrm{d}t\\) using the residue theorem.",
"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... | 12.465 degrees |
[
{
"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... | -$418.43 |
[
{
"content": "Use Stokes' Theorem to transform the surface integral \\( \\int_S \\text{rot}\\vec{F}\\cdot \\vec{dS} \\) into a line integral and calculate it for \\( \\vec{F}(x,y,z)=(y,z,x) \\), where \\( S \\) is the part of the paraboloid \\( z=1-x^2-y^2 \\) with \\( z\\ge 0 \\) and the normal vector has a no... | -\pi |
[
{
"content": "Evaluate the limit \\( \\lim_{h \\to 0} \\int \\vert f(x+h) - f(x) \\vert^p \\, dx \\) for a function \\( f \\in L^p \\), where \\( p \\in [1, \\infty) \\).",
"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... | 13850 |
[
{
"content": "Determine the degree of the image \\( \\nu_{n,d}(C) \\) under the Veronese map, where \\( C \\subset \\mathbb{P}^n \\) is a curve of degree \\( a \\). Is this degree simply \\( ad^n \\)?",
"role": "user"
}
] | a d |
[
{
"content": "Let $f:[1-\\epsilon,1] \\to \\mathbb{R}$ be a strictly decreasing, continuous, and strictly convex function with $f_-'(1)=0$, where $0<\\epsilon<1$. Define $g:[\\log(1-\\epsilon),0] \\to \\mathbb{R}$ by $g(x)=f(e^x)$. Is $g$ convex on some half-neighbourhood of $0$?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the smallest $n>3$ such that $(1+2+3+\\cdots+n)^2$ is a perfect fourth power.",
"role": "user"
}
] | 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... | 6.38 W |
[
{
"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... | 959.97 cups |
[
{
"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... | 15.63 g |
[
{
"content": "Given that $A + B + C + P + Q + R = 0$, find the value of the determinant:\n\\[\n\\begin{vmatrix}\n\\tan (A+P) & \\tan(B+P) & \\tan(C+P) \\\\\n\\tan (A+Q) & \\tan (B+Q) & \\tan (C+Q) \\\\\n\\tan (A+R) & \\tan (B+R) & \\tan (C+R)\n\\end{vmatrix}\n\\] for all values of $A, B, C, P, Q, R$.",
"rol... | 0 |
[
{
"content": "A cone is inverted and filled with water to 3/4 of its height. What percent of the cone's volume is filled with water? Express your answer as a decimal to the nearest ten-thousandth. (You should enter 10.0000 for $10\\%$ instead of 0.1000.)",
"role": "user"
}
] | 42.1875 |
[
{
"content": "Find all positive integers \\( n \\) such that \\( n^{4} - n^{3} + 3n^{2} + 5 \\) is a perfect square.",
"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... | 13.64% |
[
{
"content": "Solve the congruence equation $x^{11} \\equiv 10 \\pmod{33}$.",
"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... | 688 meters |
[
{
"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... | 447.0K |
[
{
"content": "Find the Lebesgue measure of the set of numbers in the interval (0,1) that contain 100 consecutive 4's in their decimal expansion.",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the principal value of the integral \\( \\int_{-\\infty}^\\infty \\frac{\\sin(2x)}{x^3} \\, dx \\) considering the third-order pole at \\( z=0 \\).",
"role": "user"
}
] | -2\pi |
[
{
"content": "Evaluate whether the limit \\( \\lim_{{(x, y)\\to(0, 0)}} \\frac{x^3-y^3}{x^2+y^2} \\) exists. If it does, find its value.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of solutions to the equation \\( h(x) = x^3 - x \\sin x - \\cos x = 0 \\).",
"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... | 54.88 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... | 7.35e-3 m |
[
{
"content": "Calculate the limit \\( \\lim_{x\\rightarrow 0}\\dfrac{e^{-\\frac{1}{x}}}{x^n} \\) where \\( n > 0 \\) is an integer.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the range of values for the real number \\( a \\) such that the domain of the function \\( f(x) = \\frac{1}{\\lg \\left(2^x + 4 \\cdot 2^{-x} - a \\right)} \\) is \\( \\mathbf{R} \\).",
"role": "user"
}
] | (-\infty, 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... | 1975 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... | 0.060J - 0.12J |
[
{
"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... | 1.03 g |
[
{
"content": "Compute the Lebesgue integral \\( \\int_{[0,\\pi/2]} f \\, d\\mu \\) where the function \\( f(x) \\) is defined as follows:\n\n\\[\nf(x) = \\begin{cases}\n\\sin(x) & \\text{if } \\cos(x) \\text{ is rational} \\\\\n\\sin^2(x) & \\text{if } \\cos(x) \\text{ is irrational}\n\\end{cases}\n\\]\n\nEvalu... | \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... | 0.0001072 |
[
{
"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... | 5.1e-5 A |
[
{
"content": "Find the kernel of the Vandermonde matrix \\( A \\) given by\n\\[\nA = \\begin{pmatrix} x_1^0 & x_1^1 & \\ldots & x_1^n \\\\ x_2^0 & x_2^1 & \\ldots & x_2^n \\\\ \\vdots & \\vdots & \\ldots & \\vdots \\\\ x_m^0 & x_m^1 & \\ldots & x_m^n \\end{pmatrix}\n\\]\nwhere \\( n < m - 1 \\) and the \\( x_i ... | \{\mathbf{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... | 5.3504% |
[
{
"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... | 43 |
[
{
"content": "Determine the number of ways to fill an \\(n \\times n\\) grid with 0's and 1's such that the sum of each row and column is even.",
"role": "user"
}
] | 2^{(n-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... | -0.407 J |
[
{
"content": "Determine whether there exists a complemented lattice that has a non-prime maximal ideal.",
"role": "user"
}
] | Yes |
[
{
"content": "Compute the surface integral \\( \\int_S -z^2-y^2-x^2 \\, dS \\) for the surface \\( S \\) defined by the equation \\( z^2 + y^2 + x^2 = 1 \\).",
"role": "user"
}
] | -4\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... | 122.09 eV |
[
{
"content": "Determine whether there exists an equivalence relation on the set of natural numbers, \\( \\mathbb{N} \\), such that there are infinitely many equivalence classes, each containing infinitely many elements.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the winding number of the function \\( f: S^1 \\to \\mathbb{C} \\setminus \\{ 0 \\} \\) given by \\( z \\mapsto 8z^4+4z^3+2z^2+z^{-1} \\) about the origin.",
"role": "user"
}
] | 4 |
[
{
"content": "Evaluate the limit: \\[ \\lim _{ x\\rightarrow 4 }{ \\frac { g\\left( x \\right) -8 }{ \\sqrt { x-3 } -1 } } \\] given that \\[ \\lim_{x\\to4}\\frac{2x-g(x)}{x-4}=2. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Let $p(z)$ be a polynomial of degree $n \\ge 2$. Determine if there exists a radius $R > 0$ such that \\( \\int_{|z|=R} \\frac{1}{p(z)} \\, dz = 0 \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit using L'Hopital's rule: $$\\lim_{x \\to \\infty} x^2\\left(\\ln\\left(1 + \\frac{1}{x}\\right) - \\frac{1}{x+1}\\right)$$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "A regular triangular prism $ABC A_1B_1C_1$ is inscribed in a sphere, with base $ABC$ and lateral edges $AA_1, BB_1, CC_1$. Segment $CD$ is a diameter of this sphere, and point $K$ is the midpoint of edge $AA_1$. Given that $CK = 2 \\sqrt{6}$ and $DK = 4$, find the volume of the prism.",
"role"... | 36 |
[
{
"content": "What is the sum of all positive integers $n$ that satisfy $$\\mathop{\\text{lcm}}[n,100] = \\gcd(n,100)+450~?$$",
"role": "user"
}
] | 250 |
[
{
"content": "Consider a square on a Cartesian plane with vertices at \\((0, 0), (0, 65), (65, 65),\\) and \\((65, 0)\\). Determine the number of ways to select two grid points inside this square (excluding its boundary) such that at least one of these points lies on the line \\(y = x\\) or \\(y = 65 - x\\), an... | 500032 |
[
{
"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... | 2.5e-18 C |
[
{
"content": "Evaluate \\( p(2012)^6 \\) where \\( p(x) = \\sqrt{x + 2 + 3\\sqrt{2x-5}} - \\sqrt{x - 2 + \\sqrt{2x-5}} \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Let $I = [0,1] \\times [0,1]$ and $E \\subset \\mathbb{R}^2$ be a set of zero Lebesgue measure. Determine whether the following statement is true: $$\\overline{I \\setminus E} = I.$$",
"role": "user"
}
] | True |
[
{
"content": "Does the meromorphic continuation of \\(\\frac{1}{\\zeta(z)}\\) for \\(0 \\leq \\sigma < \\frac{1}{2}\\) depend on the validity of the Riemann Hypothesis? Answer yes or no.",
"role": "user"
}
] | No |
[
{
"content": "Find the optimal solution for the following optimization problem:\n\\[\\begin{aligned} &\\text{Minimize: } \\frac{1}{N}\\left(\\sum_{i=1}^{N} w_{i}\\right)^{2} \\\\\n&\\text{Subject to: } \\|\\mathbf{w}\\|_{2}^{2}=N \\end{aligned}\\]\nwhere \\(w_{i} \\geq 0\\) for all \\(i\\), \\(\\mathbf{w}\\) is... | 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... | 0.57A |
[
{
"content": "What is the last digit of \\(\\operatorname{lcm}(3^{2003}-1,3^{2003}+1)\\)?",
"role": "user"
}
] | 4 |
[
{
"content": "Let $S$ denote the set of all positive integers whose prime factors are elements of $\\{2,3,5,7,11\\}$. (We include 1 in the set $S$.) If \\( \\sum_{q \\in S} \\frac{\\varphi(q)}{q^{2}} \\) can be written as \\(\\frac{a}{b}\\) for relatively prime positive integers $a$ and $b$, find $a+b$. Here, $... | 1537 |
[
{
"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... | 29.38 degree |
[
{
"content": "Evaluate the limit: $$\\lim_{T\\to \\infty}\\frac{\\int_0^T\\sin^2(s) \\exp(-s)\\int_0^s \\sin(\\sin a)\\exp(a)\\,\\mathrm{d}a\\,\\mathrm{d}s}{T}$$",
"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... | 5.46 L |
[
{
"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... | 5.82e15 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... | 5.86e+19 |
[
{
"content": "Evaluate the integral \\( \\int_0^1 f(x) \\, dx \\) where the function \\( f(x) = x + \\int_0^1 (x+t)tf(t) \\, dt \\).",
"role": "user"
}
] | \dfrac{42}{23} |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty} X_n \\), where \\( X_n = \\frac{1000^n}{\\sqrt{n!}} + 1 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the Galois group of the polynomial $x^5 + 15x + 12$ over the field $\\mathbb{Q}$.",
"role": "user"
}
] | S_5 |
[
{
"content": "Let $X$ and $Y$ be compact metric spaces, and let $\\pi: X \\to Y$ be a continuous onto map. Suppose $\\nu$ is a Borel probability measure on $Y$ such that $\\nu$-almost every $y \\in Y$ has a unique $\\pi$-preimage. Does there exist a measurable map $s: Y \\to X$ such that for $\\nu$-almost every... | 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... | 2.74 m |
[
{
"content": "Let \\( A \\) and \\( B \\) be \\( 2 \\times 2 \\) matrices such that \\( A^2 = B^2 = (AB)^2 = 0 \\). Does it follow that \\( AB = 0 \\)?",
"role": "user"
}
] | Yes |
[
{
"content": "In triangle $\\triangle PQR$, it is given that $QR^2 + PR^2 = 5PQ^2$. Let $G$ be the intersection point of medians $PM$ and $QN$. Determine the measure of $\\angle QGM$. Provide a solution using pure geometry.",
"role": "user"
}
] | 90^\circ |
[
{
"content": "Calculate the probability that a randomly arranged 4002-digit number, using only the digits 4 and 8, is divisible by 19.",
"role": "user"
}
] | \dfrac{1}{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... | $72,576 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\sum_{k=1}^n \\frac{1}{\\sqrt{4n^2-k^2}} \\]",
"role": "user"
}
] | \dfrac{\pi}{6} |
[
{
"content": "The tangent at the point \\( P(x_0, y_0) \\) to the parabola \\( y^2 = 4ax \\) meets the parabola \\( y^2 = 4a(x+b) \\) at points \\( Q \\) and \\( R \\). Find the coordinates of the midpoint of \\( QR \\).",
"role": "user"
}
] | (x_0, y_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... | 2.982 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... | 1.55 m/s^2 |
[
{
"content": "Determine the radius of convergence of the Taylor series for the function \\( g(z) = \\frac{\\sin z - z + \\frac{z^3}{6}}{\\cos z - 1} \\) centered at 0.",
"role": "user"
}
] | 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... | 33 miles/hour |
[
{
"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... | 9.54% |
[
{
"content": "Find the limit of the sequence of functions \\( f_n(x) = n(x^{1/n} - 1) \\) as \\( n \\to \\infty \\), where \\( x > 0 \\). Use the known limit \\( \\lim_{n\\to\\infty} (1 + \\frac{x}{n})^n = e^x \\) and consider the principle of taking limits inside continuous functions if applicable.",
"role... | \ln x |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} 5 \\sum_{k=1}^n \\frac{\\sqrt{4n+5k}}{n \\sqrt{n}} \\]",
"role": "user"
}
] | \dfrac{38}{3} |
[
{
"content": "If $A$, $B$ and $C$ are positive integers such that $\\frac{A\\sqrt{B}}{C} = \\frac{8}{3\\sqrt{2}}$, what is the value of $A+B+C$ given that $A$ and $C$ have no common prime factors, and $B$ has no perfect-square factors other than 1?",
"role": "user"
}
] | 9 |
[
{
"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... | 760.50 |
[
{
"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... | 1:1:1:1 |
[
{
"content": "Find an expression for the terminal velocity of a raindrop in terms of the constants k and g, given that the rate of growth of the raindrop's mass is km(t) and applying Newton's Law of Motion results in the equation (mv)' = gm, where m is the mass, v is the velocity, and g is the acceleration due ... | \dfrac{g}{k} |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{\\sin x}{(x^2+a^2)(x^2+b^2)}\\,\\mathrm{d}x \\) using elementary methods.",
"role": "user"
}
] | 0 |
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