prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the slant asymptote of the function \\( f(x) = xe^{\\frac{1}{x-2}} \\).",
"role": "user"
}
] | y = x + 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... | $64,850.00 |
[
{
"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... | 32.22 |
[
{
"content": "A laser is stationed at coordinates \\((1,2,4)\\), and it is pointing towards the mirror \\(\\pi:2x-y-z=0\\). After being reflected by the mirror, the laser hits the point \\((3,2,-2)\\). What are the coordinates of the reflection point \\(P\\) on the mirror?",
"role": "user"
}
] | (5, -2, 12) |
[
{
"content": "Find the limit of the sequence \\(S_n\\) defined as:\n\\[S_{n} = \\frac{1}{2n}+\\frac{1}{\\sqrt{4n^{2}-1}}+\\frac{1}{\\sqrt{4n^{2}-4}}+...+\\frac{1}{\\sqrt{3n^{2}+2n-1}}\\]\n\nDetermine if this sequence can be expressed as a definite integral and compute its limit as \\(n\\) approaches infinity.",... | \dfrac{\pi}{6} |
[
{
"content": "Let the real numbers \\(x_{1}, x_{2}, \\cdots, x_{1997}\\) satisfy the following conditions:\n1. \\(-\\frac{1}{\\sqrt{3}} \\leq x_{i} \\leq \\sqrt{3}\\) for \\(i=1,2,\\cdots,1997\\)\n2. \\(x_{1} + x_{2} + \\cdots + x_{1997} = -318 \\sqrt{3}\\)\n\nDetermine the maximum value of \\(x_{1}^{12} + x_{2... | 189548 |
[
{
"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... | 8.63% |
[
{
"content": "Find all homomorphisms $f: \\mathbb{Q} \\rightarrow \\mathbb{Q}^*$ such that $f(x + y) = f(x) \\cdot f(y)$ for all $x, y \\in \\mathbb{Q}$.",
"role": "user"
}
] | f(x) = 1 |
[
{
"content": "Apply Green's theorem to evaluate the line integral of the vector field \\( F(x,y) = (x+y, x-y) \\) over the positively oriented region bounded by the circle \\( x^2 + y^2 = 9 \\) and the curve \\( |x| + |y| = 1 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the minimum number of rooks required to color all cells of an \\( n \\times n \\) square grid, regardless of the initial numbering of the cells from 1 to \\( n^2 \\). A rook can be placed on any uncolored cell, and it can move horizontally or vertically to a cell with a higher number, co... | n |
[
{
"content": "Determine whether 5 is a generator of the multiplicative group of integers modulo 81, denoted as \\( \\mathbb{Z}_{81}^{\\times} \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists an affine scheme $X$ with exactly two points and dimension 1.",
"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... | 7735.74 K |
[
{
"content": "Robert has 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has an engraving of one face on one side, but not on the other. He wants to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible dis... | 630 |
[
{
"content": "Given the primitive function $F: \\mathbb{R} \\to \\mathbb{R}$ of $f(x) = e^{x^2}$, where $F(-1) = 0$, determine which of the following is true about $F(1)$: \\(\\text{A) } F(1) < 0 \\text{ B) } F(1) = 0 \\text{ C) } F(1) > 2 \\text{ D) } F(1) = 2\\).",
"role": "user"
}
] | 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... | 1/p AU = 1/(63242p) light years, where p is the parallax angle in radians. |
[
{
"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 loss |
[
{
"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... | 73e-4 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... | 57.2*10^9J |
[
{
"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... | 514.32 |
[
{
"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... | 332*10^6 m |
[
{
"content": "Determine whether a continuous function on the real numbers can have a periodic point of period 48 without having a periodic point of period 24.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the values of \\( n \\) for which the characteristic polynomial \\( \\chi_{A(n)}(X) \\) of the matrix \\( A(n) \\) has at least two real roots: one equal to the golden ratio \\( \\varphi = \\frac{1+\\sqrt{5}}{2} \\) and the other equal to its conjugate \\( \\frac{1-\\sqrt{5}}{2} \\).",
... | 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... | 4.40 |
[
{
"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... | 349.12 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... | 1.94e-3 |
[
{
"content": "If a Banach space $X$ is isometric to its first dual $X^*$, does it follow that $X$ must be reflexive? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the integer part $I$ of the expression $(8+3\\sqrt{7})^n = I + F$, where $F$ is a proper fraction, is even or odd.",
"role": "user"
}
] | odd |
[
{
"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... | h=\frac{d(u-V\sin \theta)}{V\cos \theta} |
[
{
"content": "In a regular pentagon $ABCDE$, point $M$ is the midpoint of side $AE$, and segments $AC$ and $BM$ intersect at point $Z$. Given that $ZA = 3$, find the length of $AB$. Express your answer in simplest radical form.",
"role": "user"
}
] | 3\sqrt{5} |
[
{
"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... | 82724.60 N/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... | Keynesian Phillips curve tradeoff |
[
{
"content": "Let $x, y, z$ be distinct positive integers such that \\(\\frac{\\sqrt{3} x+y}{\\sqrt{3} y+z} \\in \\mathbb{Q}.\\) Find the minimum possible value of \\(\\frac{x^{2}+y^{2}+z^{2}}{x+y+z}.\\)",
"role": "user"
}
] | 3 |
[
{
"content": "Let $X$ be a complex Banach space and $A: X \\rightarrow \\mathbb{C}^n$ be a continuous linear operator. If $B_X = \\{x \\in X : \\|x\\| \\leq 1\\}$ denotes the closed unit ball in $X$, is the image $A(B_X)$ necessarily compact in $\\mathbb{C}^n$?",
"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... | CHO_2 |
[
{
"content": "Find all continuous and bounded functions \\( g \\) such that for all real numbers \\( x \\), the following equation holds:\n\\[ 4g(x) = g(x+1) + g(x-1) + g(x+\\pi) + g(x-\\pi) \\]",
"role": "user"
}
] | g(x) = 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... | 25/16 ft |
[
{
"content": "Determine whether $29^{576} - 1$ is divisible by $2016$ without performing the actual calculation.",
"role": "user"
}
] | Yes |
[
{
"content": "How many ways are there to partition the set \\([8]\\) into 3 disjoint pairs? For example, one such partition is \\((12)(45)(67)\\).",
"role": "user"
}
] | 420 |
[
{
"content": "In a complete, separable, compact geodesic metric space $(M,d)$, is it true that for any point $x \\in M$, there exists an $\\varepsilon' > 0$ such that all $\\varepsilon$-balls around $x$ for $\\varepsilon < \\varepsilon'$ are convex?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the asymptotic complexity of the recurrence relation \\( T(n) = 2T(n/2) + T(n/4) + n^2 \\). Is the solution \\( \\Theta(n^2) \\)?",
"role": "user"
}
] | \Theta(n^2) |
[
{
"content": "Find the value of the limit: $$\\lim_{n\\to \\infty} \\sum_{j=n}^{4n} {4n \\choose j}\\left(\\frac{1}{4}\\right)^j \\left(\\frac{3}{4}\\right)^{4n-j}.$$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Let X and Y be two independent random variables, each uniformly distributed on the interval [0,1]. Find the probability density function (pdf) of the random variable Z, where Z = XY.",
"role": "user"
}
] | -\ln 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... | $150,534.29 |
[
{
"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... | Centralized |
[
{
"content": "Find the angle \\( \\theta \\) in the range \\( 0 \\leq \\theta < 360 \\) degrees that minimizes the x-coordinate of the Archimedean spiral given by \\( r = 1 - \\frac{0.5}{2\\pi}\\theta \\).",
"role": "user"
}
] | 174 |
[
{
"content": "Let $p$ be an odd prime and $d$ be a natural number such that $d \\mid (p-1)$. If $a^{\\frac{p-1}{d}} \\equiv 1 \\pmod{p}$, does there always exist an integer $x$ such that $x^d \\equiv a \\pmod{p}$? Answer \"Yes\" or \"No\".",
"role": "user"
}
] | Yes |
[
{
"content": "Consider a permutation of the numbers $1, 2, 3, \\ldots, 2020$ denoted by $a_1, a_2, \\ldots, a_{2020}$. Determine the number of permutations such that the absolute difference between each term and its position is constant, i.e., $|a_1 - 1| = |a_2 - 2| = \\ldots = |a_{2020} - 2020|$. Provide your ... | 9 |
[
{
"content": "Determine the number of real solutions to the equation \\( f(f(f(f(x)))) = \\frac{1}{\\sqrt{2}} \\), where \\( f(x)=\\frac{1}{(1-x^{2011})^{\\frac{1}{2011}}} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Given the integral \\( \\int_{0}^{1} (2x^2-3f(x))f(x)\\,dx=\\frac{1}{15} \\), find the value of \\( \\int_{0}^{1} f(x)\\,dx \\).",
"role": "user"
}
] | \dfrac{1}{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... | 176.78 N |
[
{
"content": "Find the minimum natural number \\(m\\) such that the limit \\(\\lim_{(x,y)\\to(0,0)} \\frac{x^{\\frac{m}{3}}|x-y|}{\\sqrt{x^2+y^2}}\\) exists and is a real number.",
"role": "user"
}
] | 1 |
[
{
"content": "Under the assumptions that $Z \\to X$ is a closed immersion of schemes and both $\\mathcal{O}_Z$ and $\\mathcal{O}_X$ are coherent sheaves of $\\mathcal{O}_Z$, resp. $\\mathcal{O}_X$-modules, is it true that if $\\mathcal{F}$ is a finitely presented quasi-coherent $\\mathcal{O}_Z$-module, then $i_... | Yes |
[
{
"content": "Evaluate the limit: $$\\lim _{t\\to 0}\\frac{\\sqrt{1+t^2}-\\sin{t}}{t^4}$$",
"role": "user"
}
] | \infty |
[
{
"content": "Determine whether the following statement is true or false: For any two vectors $u=(u_1,u_2,\\ldots,u_n)$ and $v=(v_1,v_2,\\ldots,v_n)$ in $\\mathbb{R}^n$ with $|v_i| > |u_i|$ for all $i$, and for any vector norm $\\| \\cdot\\|$ on $\\mathbb{R}^n$, it holds that $\\|v\\| > \\|u\\|$.",
"role": ... | False |
[
{
"content": "Evaluate the integral \\( \\iint \\operatorname{curl}(F) \\, dS \\) using Stoke's Theorem, where \\( F(x,y,z) = \\langle x^2z^2,y^2z^2,xyz\\rangle \\) and \\( S \\) is the part of the paraboloid \\( z=x^2+y^2 \\) that lies inside the cylinder \\( x^2+y^2=4 \\), oriented upward.",
"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... | 3.37e23 |
[
{
"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... | 5.08 m |
[
{
"content": "Evaluate the integral \\( \\int |z| \\, dz \\) along the path defined by the semicircle \\(|z|=1\\) with \\(-\\frac{\\pi}{2} \\leq \\arg z \\leq \\frac{\\pi}{2}\\), starting from \\(z=-i\\).",
"role": "user"
}
] | 2i |
[
{
"content": "Evaluate the double integral \\( J = \\iint_R (x^2-xy)\\,dx \\,dy \\), where the region \\( R \\) is bounded by the curves \\( y = x \\) and \\( y = 3x - x^2 \\).",
"role": "user"
}
] | -\dfrac{8}{15} |
[
{
"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... | 1022 g |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} 2 \\frac{(\\cosh x - 1)^{1/x^2}}{x^2} \\]",
"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... | 0.0466 rad/s |
[
{
"content": "Determine whether the congruence $x^2 \\equiv 1 \\pmod{n}$, where $n$ is a composite number, can have more than two solutions, given that $x^2 \\equiv 1 \\pmod{p}$ has at most two solutions when $p$ is a prime number.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the function $f(x)$ that satisfies $f'(0) = 1$, $-1 < f(x) < 1$, and $f(x+y) = \\frac{f(x) + f(y)}{1 + f(x)f(y)}$ for all $x \\in \\mathbb{R}$. Then, determine the limit $\\lim_{x\\to\\infty} f(x)^x$. Provide your answer as a single value.",
"role": "user"
}
] | 1 |
[
{
"content": "Find \\( \\limsup_{n\\to\\infty}\\left(\\frac{2\\cdot5\\cdot8\\cdot\\cdots\\cdot(3n-4)}{3^nn!}\\right)^{\\frac{1}{n}} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the surface area of the portion of the plane \\( z = 3 - 3y - 5x \\) that is contained within the cylinder \\( x^2 + y^2 = 16 \\).",
"role": "user"
}
] | 16\sqrt{35}\pi |
[
{
"content": "Let $F = \\{E_1, E_2, \\ldots, E_n\\}$ be a collection of $n$ subsets of a set $X$, where $n$ is a positive integer. Determine the number of distinct sets in the sigma-algebra $\\sigma(F)$ generated by $F$. Provide your answer as a single integer.",
"role": "user"
}
] | 2^{2^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-ethyl-heptan-3-ol |
[
{
"content": "In a locally compact topological space $X$, consider a compact set $C \\subset X$ and a boundary point $x \\in C$. Does there exist a neighborhood $U$ of $x$ such that $x \\in U \\subset C$? Answer yes or no.",
"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... | 2.815e-17 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... | 348 kJ/kg |
[
{
"content": "Evaluate the convolution integral \\( \\int_{-\\infty}^{+\\infty} \\delta'(a-t) g(t) \\, dt \\) given that \\( \\int_{-\\infty}^{+\\infty} \\delta'(t) g(t) \\, dt = -g'(0) \\).",
"role": "user"
}
] | g'(a) |
[
{
"content": "Determine the limit of the solution to the initial value problem $x'(t)=x^2-x$, $x(0)=\\frac{1}{3}$ as $t\\rightarrow\\infty$, if it exists.",
"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... | 3.61e-3 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\left(\\frac{n^2 + 1}{n - 1}\\right)^{-2n^2} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "There are two natural ways to inscribe a square in a given isosceles right triangle. If it is done as in Figure 1 below, then one finds that the area of the square is $441 \\text{cm}^2$. What is the area (in $\\text{cm}^2$) of the square inscribed in the same $\\triangle ABC$ as shown in Figure 2 ... | 392 |
[
{
"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... | 0.125 g/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... | 0.4s |
[
{
"content": "Calculate the limit: $$\\lim_{n\\to\\infty}\\frac{5n^n}{3n!+3^n}$$",
"role": "user"
}
] | \infty |
[
{
"content": "Evaluate the integral \\( \\int_{|z|=1} \\frac{2+\\sin(z)}{z} \\, dz \\) where the contour is the unit circle traversed once counterclockwise.",
"role": "user"
}
] | 4\pi i |
[
{
"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... | positive |
[
{
"content": "Determine the minimum number of variables required to construct a sentence in a first-order logic language consisting solely of the equality predicate \"=\" that is valid in a structure if and only if the structure's domain contains exactly n elements.",
"role": "user"
}
] | n+1 |
[
{
"content": "Determine the order of the alternating group $A_6$. Show that the order is given by \\( \\frac{6!}{2} = 360 \\).",
"role": "user"
}
] | 360 |
[
{
"content": "Let $X$, $Y$, and $Z$ be independent random variables uniformly distributed on the interval $(0,1)$. Calculate the probability that $X + Y > Z$. Express your answer as a single probability value.",
"role": "user"
}
] | \dfrac{5}{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... | 83600 |
[
{
"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... | 7500 |
[
{
"content": "Let G be a nontrivial finite group. Does there exist an irreducible representation of G over an arbitrary field with a dimension greater than or equal to the cardinality of G?",
"role": "user"
}
] | No |
[
{
"content": "The 16 positive factors of 2010 can be arranged into a 4x4 multiplicative magic square. Determine the common product of each row, column, and diagonal in this square.",
"role": "user"
}
] | 4040100 |
[
{
"content": "Evaluate the contour integral \\( \\oint_L \\frac{\\cos^2 z}{z^2}\\,dz \\) where \\(L\\) is the closed loop that goes counterclockwise around the square with vertices \\(-1\\), \\(-i\\), \\(1\\), and \\(i\\).",
"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... | 62.9 W |
[
{
"content": "Consider a binary code where the digit 0 eliminates 30% of the search space and occurs with a probability of 0.7, while the digit 1 eliminates 70% and occurs with a probability of 0.3. Is this coding scheme, on average, as efficient as a code where both 0 and 1 have equal probabilities and each ha... | No |
[
{
"content": "Compute the value of the 30th derivative of the function \\( g(x) = \\sinh{\\left(x^4\\right)} \\) at the origin, i.e., find \\( g^{(30)}(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... | 8.288% |
[
{
"content": "Evaluate the integral \\( \\int_{-27}^{-8} \\frac{dx}{x + x^{2/3}} \\) using an appropriate substitution.",
"role": "user"
}
] | -3 \ln 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... | Date Account Title and Explanation Debit Credit
October 31 Fees Income 21,500
Income Summary 21,500
To close all revenue accounts to income summary
Income Summary 14,350
Salaries Expense 11,000
Rent Expense 1,150
Supplies Expense 550
Utilities Expense 650
Depr. Exp. -Equip. 1,000
To close all expense accounts to income summary
Income Summary 7,150
Jason Jamison, Capital 7,150
To close income summary account to the capital account
Jason Jamison, Capital 2,250
Jason Jamison, Drawing 2,250
To close drawing account to the capital account |
[
{
"content": "Find the value of \\( S(S(S(S(2018^{2018})))) \\), where \\( S(n) \\) denotes the digit sum of the integer \\( n \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Determine all possible values of the positive constant \\( k \\) such that the series \\( \\sum_{n=1}^{\\infty}\\ln\\left(1+\\frac{1}{n^k}\\right) \\) converges.",
"role": "user"
}
] | k > 1 |
[
{
"content": "Find the period of the sinusoidal function given by:\n\\[ x(t) = \\cos\\left(\\frac{4\\pi t}{5}\\right)\\sin^2\\left(\\frac{8\\pi t}{3}\\right) \\]",
"role": "user"
}
] | \dfrac{15}{2} |
[
{
"content": "Determine whether the function \\( f(x, y) = \\frac{xy}{\\sqrt{x} + y^2} \\) for \\( x, y \\neq 0 \\) and \\( f(0, 0) = 0 \\) has a continuous limit at the origin \\((0,0)\\).",
"role": "user"
}
] | 0 |
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