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... | 0.079 rev/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.854 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... | Year 1: $48,920
Year 2: $49,000
Year 3: $48,160
Year 4: $46,320
Total: $192,400 |
[
{
"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... | 3413.9kg |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0^+} \\frac{1}{\\ln x} \\sum_{n=1}^{\\infty} \\frac{x}{(1+x)^n - (1-x)^n}. \\]",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "Find the radius of convergence for the power series \\( \\sum_{n=1}^\\infty 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... | 3.75% |
[
{
"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... | $960,000 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\left( \\frac{n!}{n^n} \\right)^{\\frac{1}{n}} \\]",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Determine the values of $m$ for which the equation \\( e^{\\vert{x}\\vert}=m(x+1) \\) has exactly two distinct real solutions.",
"role": "user"
}
] | (-\infty, -e^2) \cup (1, \infty) |
[
{
"content": "Convert $314_{10}$ to base 6.",
"role": "user"
}
] | 1242_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... | 18.01% |
[
{
"content": "Calculate the value of the wedge product \\( 3e_1 \\wedge 4e_3((1, \\alpha, 0), (0, \\beta, 1)) \\), where \\( e_1 = (1,0,0) \\), \\( e_2 = (0,1,0) \\), \\( e_3 = (0,0,1) \\), and \\( \\alpha, \\beta \\) are irrational numbers.",
"role": "user"
}
] | 12 |
[
{
"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... | 0.0084 M |
[
{
"content": "Determine the cardinality of the set \\( S = \\{ f: \\mathbb{R} \\to \\mathbb{R} \\mid f(x) \\neq 0, \\text{ only for finitely many } x \\in \\mathbb{R} \\} \\).",
"role": "user"
}
] | \mathfrak{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... | v^2/rg |
[
{
"content": "Evaluate the complex contour integral \\( \\oint_{C(-i, 1)} \\left(\\frac{1}{(z+i)^3} - \\frac{5}{z+i} + 8\\right)\\,dz \\), where \\( C(-i, 1) \\) is a contour around the point \\(-i\\) with radius 1.",
"role": "user"
}
] | -10\pi i |
[
{
"content": "The lines $2x+3y=10$ and $2x-3y=10$ are tangents at the extremities of the same latus rectum of an ellipse centered at the origin. Determine the length of the latus rectum of this ellipse.",
"role": "user"
}
] | \dfrac{100}{27} |
[
{
"content": "Determine the number of distinct real solutions to the equation \\(f(f(x))=0\\), where \\(f(x) = x^3 - 3x + 1\\).",
"role": "user"
}
] | 7 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $89,800 |
[
{
"content": "Calculate the volume of the set \\( Q = \\{(x^3,y^3) \\mid x^2 + y^2 \\leq 1\\} \\) using iterated integrals.",
"role": "user"
}
] | \dfrac{3\pi}{8} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 23.46 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... | 27.5 V |
[
{
"content": "Consider an urn with 7 blue balls and 5 yellow balls. Balls are drawn from the urn one by one without replacement until the urn is empty. Let \\( X \\) be the number of blue balls in the first six draws, and \\( Y \\) the number of blue balls in the last six draws. Compute the covariance \\( \\tex... | -\dfrac{35}{44} |
[
{
"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... | $66,112.99 |
[
{
"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... | 20.26% |
[
{
"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... | -25/12 ft/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... | 249 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... | 135.8ms^-1 |
[
{
"content": "Determine the number of solutions to the equation \\( \\alpha_1x_1 + \\alpha_2x_2 + \\ldots + \\alpha_nx_n = 0 \\) in the vector space \\( \\mathbb{F}_p^n \\), where \\( \\mathbb{F}_p \\) is a Galois field with \\( p \\) elements and not all \\( \\alpha_i \\in \\mathbb{F}_p \\) are zero.",
"ro... | p^{n-1} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $25,479.33 |
[
{
"content": "Determine which of the following functions are metrics on a non-empty set $X$:\n\n1. $\\rho_1 (x,y) = d(x,y) d'(x,y)$ for all $x,y \\in X$.\n2. $\\rho_2 (x,y) = \\max\\{5, d(x,y)\\}$ for all $x,y \\in X$.\n3. $\\rho_3 (x,y) = \\max\\{d(x,y), d'(x,y)\\}$ for all $x,y \\in X$.\n4. $\\rho_4 (x,y) = \... | \rho_3 |
[
{
"content": "Given the equations \\(x = 3\\sqrt{y\\sqrt{3\\sqrt{y\\cdots}}}\\) and \\(y = 3\\sqrt{x\\sqrt{3\\sqrt{x\\cdots}}}\\), find the value of \\(x + y\\).",
"role": "user"
}
] | 162 |
[
{
"content": "In a right-angled triangle \\( \\triangle ABC \\) with \\( \\angle C = 90^\\circ \\), let \\( a, b, c \\) be the lengths of the sides opposite angles \\( A, B, \\) and \\( C \\) respectively. Circles \\( K \\) and \\( L \\) have their centers on sides \\( a \\) and \\( b \\), and are tangent to si... | 1 + \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... | 4.5 C |
[
{
"content": "Evaluate the limit: $$\\lim_{{x\\to0}}\\frac{1-\\frac{1}{2}x^2-\\cos\\left(\\frac{x}{1-x^2}\\right)}{x^4}$$",
"role": "user"
}
] | \dfrac{23}{24} |
[
{
"content": "Evaluate the integral: $$\\int_{\\pi/6}^{\\pi/3} \\frac {\\sqrt[3]{\\sin x}} {\\sqrt[3]{\\sin x} + \\sqrt[3]{\\cos x}}dx.$$",
"role": "user"
}
] | \dfrac{\pi}{12} |
[
{
"content": "Assume the Generalized Continuum Hypothesis (GCH) holds and \\(\\kappa\\) is a regular cardinal. Determine the number of non-isomorphic partial orders of size less than \\(\\kappa\\).",
"role": "user"
}
] | \kappa |
[
{
"content": "Determine if there exists a natural number that forms a perfect pair with 122, where both the sum and the product of the two numbers are perfect squares.",
"role": "user"
}
] | 14762 |
[
{
"content": "Calculate the integral \\( \\int_{-2}^2 \\left(x^3\\cos\\frac{x}{2}+\\frac{1}{2}\\right)\\sqrt{4-x^2}\\ dx \\) and provide the first 10 digits of the result.",
"role": "user"
}
] | 3.141592653 |
[
{
"content": "Find the distance from the vector \\((1,0,0,1)\\) to the subspace \\(L = (\\text{Sp}\\{(1,0,2,1),(3,1,4,4),(1,1,0,2)\\})^{\\perp}\\).",
"role": "user"
}
] | \dfrac{\sqrt{14}}{3} |
[
{
"content": "In the given pattern of numbers, each row \\( n \\) contains the number \\( n \\) multiple times. Determine \\( a(n) \\), the number of times the number \\( n \\) appears in the \\( n \\)-th row of the pattern.",
"role": "user"
}
] | n |
[
{
"content": "Let \\( f : \\mathbb{R} \\rightarrow \\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right) \\) be defined by \\( f(x) = \\arctan\\left(\\frac{1}{x^2+x+1}\\right) \\) for every \\( x \\in \\mathbb{R} \\). Calculate \\( \\tan\\left(\\sum_{i=1}^{21} f(i)\\right) \\).",
"role": "user"
}
] | \dfrac{21}{23} |
[
{
"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... | 671.5041667 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... | 7.6 mm |
[
{
"content": "Let \\( f :\\mathbb{R}\\to \\mathbb{R} \\) be a continuous function with period 1. Given that \\[ \\lim_{n\\to\\infty}\\int_0^1\\sin^2(\\pi x)f(nx)dx= \\frac{1}{k}\\int_0^1f(x)dx, \\] find the value of \\( k \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Compute the limit \\(\\lim_{x\\to 0^{+}}(\\cos x-1)e^{\\cot x}\\).",
"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... | 42.62 years |
[
{
"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... | 417 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... | y = 2sin(t + 0.5) ft |
[
{
"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... | $2,768.75 million |
[
{
"content": "Each of the ten cards has a real number written on it. For every non-empty subset of these cards, the sum of all the numbers written on the cards in that subset is calculated. It is known that not all of the obtained sums are integers. What is the largest possible number of integer sums that could... | 511 |
[
{
"content": "The hypotenuse of a right triangle measures 10 inches and one angle is $45^{\\circ}$. What is the number of square inches in the area of the triangle?",
"role": "user"
}
] | 25 |
[
{
"content": "Find the Taylor series of \\( f(z) = \\frac{z(z-3)}{(z-1)} \\) centered at \\( z=3 \\) and determine its radius of convergence.",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the radius of convergence $R$ for the power series $$S(x)=\\sum_{n\\geq0} \\frac{x^{4n+1}}{4n+1}+ \\sum_{n\\geq0} \\frac{x^{4n+2}}{4n+2}.$$",
"role": "user"
}
] | 1 |
[
{
"content": "Find the coefficient $a_7$ in the expansion of the product of the generating functions \\( \\frac{2}{(1-x)^2} \\) and \\( \\frac{x}{1-x-x^2} \\).",
"role": "user"
}
] | 158 |
[
{
"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... | 0.61% |
[
{
"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... | {eq}T_c = \frac{\rho V c T - m L_f}{m c + V \rho c}{/eq} |
[
{
"content": "Let $f$ be a smooth function, $f: \\mathbb{R}^2 \\to \\mathbb{R}$. Determine the Lie bracket $\\left[\\frac{\\partial}{\\partial x}, \\frac{\\partial}{\\partial y}\\right]$. What is the result?",
"role": "user"
}
] | 0 |
[
{
"content": "Given the ellipse \\(C: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1 (a>b>0)\\) with foci \\(F_{1}\\) and \\(F_{2}\\), where the focal distance is \\(2c\\). The point \\(N\\left(\\frac{3c}{2}, \\frac{\\sqrt{2}c}{2}\\right)\\) is inside the ellipse, and \\(M\\) is a point on the ellipse \\(C\\). It ... | D |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty}\\left(\\frac{\\sqrt{n^2+n}-1}{n}\\right)^{2\\sqrt{n^2+n}-1}.$$",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"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... | constant |
[
{
"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... | $679.42 |
[
{
"content": "Find the remainder when \\( \\sum_{n=1}^{2024^{2024}} f(n) \\) is divided by 1000, where \\( f(n) \\) denotes the number of divisors of \\( 2024^{2024} \\) that are either less than \\( n \\) or share at least one prime factor with \\( n \\).",
"role": "user"
}
] | 224 |
[
{
"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. mol |
[
{
"content": "Find the optimal solution to the following optimization problem using the Lagrange dual method and KKT conditions:\n\\[\n\\begin{align*}\n\\max & \\quad x^2+y^2 \\\\\n\\text{s.t.} & \\quad x^2 \\leq 1 \\\\\n& \\quad 0 \\leq y \\leq 2\n\\end{align*}\n\\]",
"role": "user"
}
] | 5 |
[
{
"content": "Suppose \\((X, \\mathcal{D})\\) is a uniform space where every complete subset is closed. Is \\((X, \\mathcal{D})\\) a Hausdorff space?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the radius of convergence for the Laurent series expansion of the function \\( f(z) = \\frac{z^2+1}{z(z-3)} \\) in the region \\( 3<|z|< \\infty \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to\\infty} \\frac{e^{-1/x^2}-1}{2\\arctan x-\\pi} \\]",
"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... | -0.19 |
[
{
"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... | 4.46 mm |
[
{
"content": "Determine the set of all numbers \\( C \\) such that the inequality \\( |\\alpha \\sin x + \\beta \\cos 4x| \\leq C \\) is satisfied for all \\( x \\) and for any \\( (\\alpha, \\beta) \\) where \\( |\\alpha| \\leq 1 \\) and \\( |\\beta| \\leq 1 \\).",
"role": "user"
}
] | [2, \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... | 58.6 mol |
[
{
"content": "Calculate the arc length of the curve defined by the equation \\(6xy - y^4 = 3\\) from the point \\(\\left(\\frac{19}{12}, 2\\right)\\) to the point \\(\\left(\\frac{14}{3}, 3\\right)\\).",
"role": "user"
}
] | \dfrac{13}{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... | 17.6 m/s |
[
{
"content": "Find the value of the infinite series \\( \\frac{3}{1!} + \\frac{5}{2!} + \\frac{7}{3!} + \\dotsb \\). Express your answer in terms of the number \\( e \\).",
"role": "user"
}
] | 3e - 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... | 1.6 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... | 2.50 atm |
[
{
"content": "Determine whether the function \\( f(n) = n^{\\log(n)} \\) is in \\( O(\\log(n)^n) \\) or not. Provide a justification for your answer.",
"role": "user"
}
] | O(\log(n)^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... | 1.40875 |
[
{
"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... | Year 1: 490,000, Year 2: 553,750 |
[
{
"content": "Find the minimum value of \\( M = \\frac{x}{x^2+1} + \\frac{y}{y^2+1} + \\frac{z}{z^2+1} \\) given that \\( x, y, z \\in \\mathbb{R} \\) and \\( x+y+z = xy+yz+xz \\).",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "Calculate the surface area of the portion of the cylinder \\(y^2+z^2=9\\) that is bounded by the cylinder \\(x^2+y^2=9\\) without using polar coordinates.",
"role": "user"
}
] | 72 |
[
{
"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... | 2.9e-5 |
[
{
"content": "Given a triangle $\\triangle ABC$ with altitudes $p_1, p_2, p_3$ from vertices $A, B, C$ respectively, and let $\\Delta$ denote the area of the triangle, and $R$ be its circumradius. Determine the value of the expression:\n$$\\frac{\\cos A}{p_1} + \\frac{\\cos B}{p_2} + \\frac{\\cos C}{p_3}$$\nGiv... | \dfrac{1}{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... | 0.836g |
[
{
"content": "Determine the value of the constant \\( k \\) such that the function \\( f(x) = \\frac{k|x|}{(1+|x|)^4} \\) is a probability density function. This requires that \\( \\int_{-\\infty}^{\\infty} f(x) \\, dx = 1 \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given real numbers $x, y, z$ such that $x^2 + 4y^2 + 16z^2 = 48$ and $xy + 4yz + 2zx = 24$, find the value of $x^2 + y^2 + z^2$. \\( \\boxed{} \\)",
"role": "user"
}
] | 21 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0} \\frac{\\int_{x^2}^{x^6}(e^{u^{5}}-1)du}{x^{20}}$$",
"role": "user"
}
] | -\infty |
[
{
"content": "Determine all real numbers \\( \\beta \\in \\mathbb{R} \\) such that the equation \\[ x(t) + \\int_0^1 (1+\\alpha ts)x(s)\\,ds = \\beta + t^2 \\] is solvable in the space \\( L_2[0,1] \\) for any real number \\( \\alpha \\in \\mathbb{R} \\).",
"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... | 205.59 kJ/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... | 12.31 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... | 525.26 K |
[
{
"content": "Find the minimum value of the function \\( f(x,z) = x(36-x^2-z^2)z \\) subject to the constraint \\( x^2 + y^2 + z^2 = 36 \\) using Lagrange's method.",
"role": "user"
}
] | -162 |
[
{
"content": "Determine whether the condition that for every point $x \\in X$, there exists a neighborhood $U$ such that the restriction $f\\rvert_U:U\\to f(U)$ is a homeomorphism, implies that the function $f:X\\to Y$ is a local homeomorphism.",
"role": "user"
}
] | No |
[
{
"content": "Let $R$ be an integral domain and $F$ its field of fractions. If $M$ is a finitely generated $F$-module, is $M$ also a finitely generated $R$-module? 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... | <img>/cimages/multimages/16/prn-13208253291466134643.png</img> |
[
{
"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... | 24.67 |
[
{
"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... | 10cm |
[
{
"content": "Compute the limit \\( \\lim_{{x \\to \\infty}} \\left( \\frac{\\left(\\sqrt{1+\\frac{x^3}{x+1}}-x\\right)\\ln x}{x\\left(x^{\\frac{1}{x}}-1\\right)+\\sqrt{x}\\ln^2x} \\right) \\) without using L'Hopital's rule.",
"role": "user"
}
] | 0 |
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