prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the limit of the sequence \\( \\lim_{n \\to \\infty} \\frac{n!}{a^{n + 1}} \\) where \\( a \\) is a positive real number, without using Stirling's approximation.",
"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... | 0.474 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... | 3IO3-(aq) + 24I-(aq) + 18H+(aq) -> 9I3-(aq) + 9H2O(l) |
[
{
"content": "Evaluate the limit \\( \\lim \\limits_{x \\to 0^+} \\frac{\\sin^{-1}(1 - x) \\times \\cos^{-1}(1 - x)}{\\sqrt{2x}\\times(1 - x)} \\) where \\( \\{x\\} = x \\) for this problem. Given that \\( \\lim \\limits_{x \\to 0^+} \\frac{\\sin^{-1}(1 - x)}{1 -x} = \\frac{\\pi}{2} \\), find the value of the l... | \dfrac{\pi}{2} |
[
{
"content": "Let $a, b, c$ be positive real numbers such that $abc = 1$. Determine the maximum value of the expression:\n\\[ \\frac{a}{a^8+1} + \\frac{b}{b^8+1} + \\frac{c}{c^8+1}. \\]",
"role": "user"
}
] | \dfrac{3}{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... | 0.235 |
[
{
"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... | 128,640 lbs |
[
{
"content": "Determine whether the radius of convergence of the Taylor series of the function \\( f(z)=\\frac{1}{1+e^z} \\) centered at \\( z=0 \\) is \\( \\pi \\).",
"role": "user"
}
] | \pi |
[
{
"content": "Determine the real number $y$ such that the inequality \\( \\frac{a+c}{b+d} \\geq y \\cdot \\left ( \\frac{a}{b} + \\frac{c}{d} \\right) \\) holds for all real numbers $a, b, c, d$ where $a, c \\geq 0$ and $b, d > 0$. Provide your answer as a single real number.",
"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... | -23.5 N/C |
[
{
"content": "Find the polynomial \\( p(x) \\) such that \\( p(x) = p(x+3) \\) for all \\( x \\).",
"role": "user"
}
] | c |
[
{
"content": "A car has four tires, each with an exponential lifetime averaging 5000 miles, and one spare tire with an exponential lifetime averaging 1000 miles. When a primary tire fails, the spare is used. Calculate the expected number of miles the car can travel before any of the remaining three primary tire... | 1875 |
[
{
"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... | 23.8 |
[
{
"content": "Evaluate the limit \\(\\lim_{n\\to\\infty} \\frac{\\prod_{k=1}^n (1-\\frac{1}{k})}{n}\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether an integral domain with non-commutative multiplication can be a Unique Factorization Domain (UFD).",
"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... | 0.1 kg |
[
{
"content": "Evaluate the definite integral: \\[ \\int_0^{2\\pi} \\frac{dx}{\\sin^{4}x + \\cos^{4}x} \\]",
"role": "user"
}
] | 2\sqrt{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... | 5.36e-12 |
[
{
"content": "Determine whether the inequality \\( S = \\sum_{i,j=1}^n \\frac{a_i a_j}{i+j} \\ge 0 \\) holds for any sequence \\((a_1, a_2, \\ldots, a_n) \\in \\mathbb{R}\\).",
"role": "user"
}
] | S \geq 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... | MgO(s) + H_2(g) + Delta rarr Mg(s) + H_2O(g) |
[
{
"content": "100 people who were surveyed and asked the question: ``Is fuchsia kinda pink, or purply?'' Of them, 60 believe that fuchsia is ``kinda pink'' and 27 believe it is both ``kinda pink,'' and also ``purply.'' Another 17 think that fuchsia is neither ``kinda pink'' nor ``purply.''\n\nHow many of those... | 50 |
[
{
"content": "Let $A$ be a $k$-algebra and $l/k$ be a finite field extension of $k$. Suppose $A \\otimes_k l$ is an integral domain. Does it follow that the map $A \\rightarrow A \\otimes_k l$ defined by $a \\mapsto a \\otimes 1$ is injective?",
"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... | 1.176J |
[
{
"content": "Determine whether the embedding of \\( \\mathcal{l}^1 \\) into \\( \\mathcal{l}^p \\) is continuous for any \\( p \\geq 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... | 45185.58 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $1.79 |
[
{
"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... | $ 39,184 |
[
{
"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... | 0.037 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... | 18.33 degrees |
[
{
"content": "Compute the expectation of the random variable $X$ with the cumulative distribution function (CDF) given by \\[ F_X(x) = \\frac{1}{27}\\min\\{\\lfloor x\\rfloor, 3\\}^3 \\] for $x \\geq 0$. Consider any issues that may arise with the derivative of the floor function.",
"role": "user"
}
] | \dfrac{8}{3} |
[
{
"content": "Is every totally disconnected space a discrete topology?",
"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... | 51.7 hours |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty} \\frac{n}{\\ln(n)}\\left(n^{1/n}-1\\right) \\]",
"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... | -2114158.16 |
[
{
"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... | 8.08e-11 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... | 47,723.07, The buyer pays the seller |
[
{
"content": "Calculate the surface area of the surface $S$ that lies above the region $\\Omega$ in the $(xy)$-plane, bounded by the circle $x^2 + y^2 \\leq a^2$, where $a$ is a constant. Given the conditions $|\\frac{\\partial z}{\\partial x}| \\leq 2$ and $|\\frac{\\partial z}{\\partial y}| \\leq 2$, use the ... | 3\pi 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... | 1.6e+04 nC |
[
{
"content": "Evaluate the integral: $$\\int_0^1 \\sqrt{\\frac{1-x^2}{x+2x^3+x^5}}\\,dx$$ using Euler's integral.",
"role": "user"
}
] | \dfrac{\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... | HCl > HF > HClO > C_6H_6O |
[
{
"content": "Given the parabola \\( y^2 = 4x \\), a line passing through its focus \\( F \\) intersects the parabola at points \\( M \\) and \\( N \\). Let \\( E(m,0) \\) be a point on the x-axis. The extensions of \\( ME \\) and \\( NE \\) intersect the parabola again at points \\( P \\) and \\( Q \\), respec... | 3 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{{x \\to \\infty}} \\left(\\frac{{1+x^2}}{{x+x^2}}\\right)^{2x}. \\]",
"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... | $2,453.60 |
[
{
"content": "Evaluate the integral \\( \\iiint_{[0,1]^n} \\max \\{u_1,u_2,...,u_n\\} \\,du_1 \\dots du_n \\).",
"role": "user"
}
] | \dfrac{n}{n+1} |
[
{
"content": "Find the number of ordered pairs \\((m, n)\\) of positive integers that satisfy the equation \\(4^m - 3^n = 1\\).",
"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... | 65Nm |
[
{
"content": "Find the length of the curve given by the polar equation \\( r = a\\cos(\\theta) \\). Assume \\( a \\) is positive.",
"role": "user"
}
] | \pi a |
[
{
"content": "We have a standard deck of 52 cards, with 4 cards in each of 13 ranks. We call a 5-card poker hand a full house if the hand has 3 cards of one rank and 2 cards of another rank (such as 33355 or AAAKK). What is the probability that five cards chosen at random form a full house?",
"role": "use... | \frac{6}{4165} |
[
{
"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... | 0.363 |
[
{
"content": "In a flow network with a source, a sink, and $n$ internal nodes, each arc from the source to an internal node and from an internal node to the sink has a capacity of 2. Determine the number of different cuts with minimum capacity in this network.",
"role": "user"
}
] | 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... | Economy |
[
{
"content": "Let \\( f(z)=\\sin(z+\\mathrm{e}^{3z}) \\). Compute the Wirtinger derivative \\( \\frac{\\partial f}{\\partial \\bar{z}}(z) \\) using the Wirtinger derivative operator:\n\\[\n\\frac{\\partial}{\\partial \\bar{z}} = \\frac{1}{2} \\left( \\frac{\\partial}{\\partial x} + \\mathrm{i} \\frac{\\partial}... | 0 |
[
{
"content": "Find the determinant of the $n \\times n$ matrix given by:\n\\[\nD_n = \\left| \n \\begin{matrix}\n n & -1 & -3 & 0 & 0 & \\cdots & 0 & 0 & 0 \\\\\n n & 1 & 2 & -3 & 0 & \\cdots & 0 & 0 & 0 \\\\\n n & 0 & 1 & 2 & -3 & \\cdots & 0 & 0 & 0 \\\\\n n & 0 & 0 & 1 & 2 & \\cdots & 0 & ... | n^2 |
[
{
"content": "If $|z| = 1$, express $\\overline{z}$ as a simplified fraction in terms of $z$.",
"role": "user"
}
] | \frac{1}{z} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.38 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... | $40.73 |
[
{
"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... | 0.552 eV |
[
{
"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... | $2,082,890 |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty}\\left( \\frac{1}{\\sqrt{n^3+1}} + \\frac{1}{\\sqrt{n^3+4}} + \\cdots + \\frac{1}{\\sqrt{n^3+n^2}}\\right)$$",
"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... | 102000 |
[
{
"content": "Approximate \\( \\arctan\\frac{8}{9} \\) using a first-order Taylor expansion around \\( \\arctan 1 \\). How many digits of accuracy can you guarantee in your approximation?",
"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... | $31,500.00 |
[
{
"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... | Rich Alumni |
[
{
"content": "Determine the cardinality of the set of all Well Formed Formulas (WFFs) in propositional logic, given the following grammar: $P_n$ is a WFF for every $n \\in \\mathbb{N}$, $(\\phi \\rightarrow \\psi)$ is a WFF when $\\phi$ and $\\psi$ are WFFs, and $\\neg \\phi$ is a WFF when $\\phi$ is a WFF.",
... | \aleph_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... | 0.055 m |
[
{
"content": "Find the minimum value of the function \\( f(x) = \\int_{0}^{1} |x-t|^3 \\, dt \\) for \\( x \\in \\mathbb{R} \\).",
"role": "user"
}
] | \dfrac{1}{32} |
[
{
"content": "Determine the constant \\( A \\) such that the surfaces \\( x^2 + y^2 + 2z^2 = A \\) and \\( xy + z^2 = 2 \\) have a common tangent plane at the same point.",
"role": "user"
}
] | 4 |
[
{
"content": "If the line \\(y = kx + n\\) is a common tangent to the circle \\(x^2 + y^2 = 4\\) and the ellipse \\(2x^2 + 5y^2 = 10\\), find the value of \\(k^2 + n^2\\).",
"role": "user"
}
] | 14 |
[
{
"content": "Is there a finite distributive lattice $L$ such that there is no injective lattice homomorphism $f: L \\to \\omega^\\omega$, where $\\omega^\\omega$ is considered as a lattice with component-wise join and meet?",
"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... | 5.96e22 iron atoms |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty}\\sum_{k=1}^n\\sin\\left(\\frac{k^2}{n^3}\\right) \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Find the residue of the function \\( \\frac{z}{\\log{z}} \\) at the point \\( z=1 \\).",
"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... | Organic scintillators |
[
{
"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... | 2.33 |
[
{
"content": "Calculate the mass of a solid body in the first octant, bounded by the planes $z = 0$, $y = 0$, $z = y$, and the parabolic cylinder $y = 4 - x^2$, with a density function given by $\\rho = xz$. What is the mass of the solid?",
"role": "user"
}
] | \dfrac{16}{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... | 9.13e-21 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... | 141 N |
[
{
"content": "A plane $P$ is parmeterized by\n\\[\\mathbf{v} = \\begin{pmatrix} 1 \\\\ 6 \\\\ 7 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ -1 \\\\ -1 \\end{pmatrix} + s \\begin{pmatrix} 2 \\\\ -3 \\\\ -5 \\end{pmatrix},\\]and line $L$ is parameterized by\n\\[\\mathbf{w} = \\begin{pmatrix} 7 \\\\ 4 \\\\ 1 \\end{... | \begin{pmatrix} 1 \\ 4 \\ 3 \end{pmatrix} |
[
{
"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... | $\sqrt {\dfrac{4g}{3R}}$ |
[
{
"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... | 99 |
[
{
"content": "Find $x$ such that $\\lfloor x \\rfloor + x = \\dfrac{13}{3}$. Express $x$ as a common fraction.",
"role": "user"
}
] | \dfrac{7}{3} |
[
{
"content": "Is the space $C([0, 1], [0, 1])$ of continuous functions from $[0, 1]$ to $[0, 1]$ dense in the space $\\Pi_{[0, 1]}[0, 1]$ of all such functions with respect to pointwise convergence?",
"role": "user"
}
] | Yes |
[
{
"content": "Compute the integral \\( \\iiint_V \\nabla \\cdot \\vec{G} \\, dV \\) using Gauss's divergence theorem, where \\( \\vec{G} = (y^2z, x − yz^2, x^2) \\) and \\( V \\) is the region bounded by the paraboloid \\( z = x^2 + y^2 \\) and the plane \\( z = 4 \\).",
"role": "user"
}
] | -64\pi |
[
{
"content": "Determine whether the following statement is true or false: Given a topological space $X$ and subsets $U$ and $W$ such that $U$ is open and $W \\subseteq U$, if $X$ is locally connected and $W$ is connected, then there exists an open and connected subset $V$ of $X$ such that $W \\subseteq V \\subs... | 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... | $24,320 |
[
{
"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... | 1613.4 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... | 2.14 |
[
{
"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... | 279 N |
[
{
"content": "Show that using the Poisson distribution, \\( \\lim_{n \\to +\\infty} e^{-n} \\sum_{k=1}^{n}\\frac{n^k}{k!} = \\frac {1}{2} \\).",
"role": "user"
}
] | \dfrac{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... | 5.5e11 N/C |
[
{
"content": "A rectangular box has one corner at the origin and the opposite corner on the plane \\(x + 2y + 3z = 6\\). The edges of the box are parallel to the coordinate axes. What is the maximum possible volume of the box?",
"role": "user"
}
] | \dfrac{4}{3} |
[
{
"content": "Evaluate the convergence of the improper integral \\( \\int_{0}^{\\infty} \\frac{\\ln x}{1+x^{2}} \\, dx \\) and determine its value if it converges.",
"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... | $ 402,299 |
[
{
"content": "Find the limit of the series \\( \\sum_{k=0}^\\infty \\frac{h^{2k}}{k! k!} \\).",
"role": "user"
}
] | I_0(2h) |
[
{
"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... | -257.21 km/hr |
[
{
"content": "Let $f: \\mathbb{R} \\rightarrow S$ be a surjective ring homomorphism. If $\\mathbb{R}$ is a principal ideal domain (PID), does it follow that $S$ is a principal ideal ring (PIR)? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine all functions \\( f: \\mathbb{Q} \\rightarrow \\mathbb{Q} \\) such that for all rational numbers \\( x \\) and \\( y \\), the equation \\( f(x+y) = f(x) + f(y) \\) holds.",
"role": "user"
}
] | f(x) = ax |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $51.82 million |
[
{
"content": "Given \\(\\left[\\prod_{k=1}^{n} \\frac{(2k+1)^{4}+(2k+1)^{2}+1}{(2k)^{4}+(2k)^{2}+1}\\right] = 44\\), find the value of \\(n\\). Here, \\([x]\\) denotes the greatest integer less than or equal to the real number \\(x\\).",
"role": "user"
}
] | 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... | 58.19 mol |
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