prompt list | ground_truth string |
|---|---|
[
{
"content": "Verify if the following ordinary differential equation (ODE) and its solution are correct for the process $Z_T = e^{2 \\sqrt{2}(W_T - W_t)}$ using Ito's lemma:\n\n1. Differential for $dZ_T$:\n $$dZ_T = 2\\sqrt{2}Z_T\\,dW_T + 8Z_T\\,dT$$\n\n2. Integrating and taking expectations:\n $$E(Z_T) = 1... | e^{4(T - t)} |
[
{
"content": "What is the sum of all of the odd divisors of $180$?",
"role": "user"
}
] | 78 |
[
{
"content": "Find the number of zeroes of the function \\(f(z) = z^4 - 3z^2 + 3\\) that lie in the first quadrant of the complex plane.",
"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... | 1.49 |
[
{
"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... | -0.042 m |
[
{
"content": "Determine the value of \\( \\lambda \\) for which the improper integral \\[ I = \\int_{0}^{\\infty} \\left(\\frac{x+1}{3x^2 + \\lambda} - \\frac{\\lambda}{2x+1}\\right)dx \\] converges to a finite number.",
"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... | 1.26 m/s |
[
{
"content": "Calculate the value of the summation: \\[ \\sum_{k=0}^{n} (-1)^k \\binom{n}{k} \\binom{2n-2k}{n} \\]",
"role": "user"
}
] | 2^n |
[
{
"content": "Determine all local extreme points of the function \\( f(x,y) = x^2y^2 + x^2y + 2y^2 - 4y \\).",
"role": "user"
}
] | (0, 1) |
[
{
"content": "Find the maximum area of the triangle PQR formed by the tangent line to the curve \\( f(t) = -\\ln(t) \\) at a point \\( P(t, -\\ln(t)) \\) where \\( 0 < t < 1 \\), with points Q and R lying on the x-axis.",
"role": "user"
}
] | \dfrac{2}{e^2} |
[
{
"content": "Determine the number of invertible $3 \\times 3$ matrices over $\\mathbb{Z}/3\\mathbb{Z}$ that commute with the matrix $A = \\begin{pmatrix} 2 & 0 & 0 \\\\ 0 & 2 & 0 \\\\ 0 & 0 & 1 \\end{pmatrix}$. Provide your answer as a single integer.",
"role": "user"
}
] | 96 |
[
{
"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... | -122.80 |
[
{
"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... | 23.27 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... | $31.78 |
[
{
"content": "Evaluate the limit: $$ \\lim_{n\\to\\infty}\\frac{n\\cdot \\sin\\left(\\frac{2}{n}\\right)\\cdot \\ln\\left(1+\\frac{3}{n^2}\\right)} {\\left(1+\\frac{3}{n^2}\\right)^n\\cdot \\left(1-\\cos\\left(\\frac{1}{n}\\right)\\right)} $$",
"role": "user"
}
] | 12 |
[
{
"content": "Determine the number of 4-digit numbers such that if any single digit is removed, the resulting 3-digit number divides the original 4-digit number.",
"role": "user"
}
] | 14 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 344.8 K |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.67e4 nuclei |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2C3H8 + 13O2 --> 6CO3 + 8H2O |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0}\\frac{x-\\int_{0}^{x}\\cos u^2\\,du}{6\\sin^{-1}x-6x-x^3}$$",
"role": "user"
}
] | \dfrac{2}{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... | 9.39 g |
[
{
"content": "Find the value of \\(\\sigma\\) for a Gaussian distribution centered at 0 such that 90% of the distribution's integral is within the interval \\([-10, 10]\\).",
"role": "user"
}
] | 6.08 |
[
{
"content": "Find the equilibrium temperature distribution in a rod of length $l$ given by the equation:\n\\[ 0 = ku_{xx} - hu, \\quad 0 < x < l \\]\nwith boundary conditions:\n\\[ u(0) = 0, \\quad u(l) = 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... | 56 cm |
[
{
"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... | 121.07 |
[
{
"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... | 0.703 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... | -55 cm |
[
{
"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... | 21% |
[
{
"content": "Evaluate the limit: \\[ \\lim_{m \\to \\infty} \\frac{\\int_{0}^{m}t^{m-1}e^{-t}dt}{(m-1)!} = \\frac{\\gamma(m,m)}{\\Gamma(m)}, \\qquad m \\in \\mathbb{Z^{+}} \\] where \\(\\gamma(s,x)\\) is the lower incomplete gamma function, and \\(\\Gamma(s)\\) is the ordinary gamma function. Verify that this ... | \dfrac{1}{2} |
[
{
"content": "Evaluate the integral \\( \\int \\frac{z}{z^2+1} \\, dz \\) over the contour bounding the rectangle defined by \\(-1 < x < 1\\) and \\(-2 < y < 2\\), oriented counterclockwise.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Determine whether there exists a non-holomorphic but real differentiable function $f : D^2 \\setminus \\{0\\} \\to \\mathbb{R}$ such that $xf(x) \\to 0$ as $x \\to 0$, but $f(x)$ is not bounded near 0.",
"role": "user"
}
] | Yes |
[
{
"content": "Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the largest triangle is 8 centimeters. What is the number of centimeters in the length of the longer leg of the smallest triangle? Express your answer as a common f... | \frac{9}{2} |
[
{
"content": "Determine the radius of convergence of the power series representation of the function \\( \\frac{\\tan(\\frac{z}{2})}{(z+2)(z+3)} \\) around \\( z = 0 \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Calculate the residue of the function \\( \\frac{1}{\\cos^2 z} \\) at the point \\( z = \\frac{\\pi}{2} + \\pi k \\), where \\( k \\) is an integer.",
"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... | 0.06392 m |
[
{
"content": "Find the inverse of the element \\((x+2) + I\\) in the quotient ring \\(\\mathbb{Z}_5[x]/I\\), where \\(I\\) is the ideal generated by \\(b = x^3 + 3x + 2\\).",
"role": "user"
}
] | 3x^2 + 4x + 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... | 1.5 and 1.0 |
[
{
"content": "Evaluate the limit \\( \\lim_{x \\to \\infty} \\left( \\frac{P(x)}{5(x-1)} \\right)^x \\) where \\( P(x) = ax^2 + bx + c \\) with \\( a, b, c \\in \\mathbb{R} \\), \\( P(2) = 9 \\), and \\( P'(3) = 5 \\). Given that one root \\( \\alpha \\to \\infty \\), find the value of the limit.",
"role": ... | e^{\frac{4}{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... | $52,000 |
[
{
"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... | Bay City Company
Flexible Budget Performance Report for July
Actual (a) Flexible budget variance (b) - (a) Flexible budget (b) Volume variance (c) - (b) Static Budget (c)
Units manufactured and sold
4,900 4,900 6,000
Revenue
$436,100 $44,100 F = $480,000 x 4,900/6,000 = $392,000 $88,000 U $480,000
Variable cost
$270,... |
[
{
"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... | 2.033e-4 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... | 9.21% |
[
{
"content": "Given a set \\( S = \\{1, 2, 3, \\cdots, N\\} \\) and four 500-element subsets \\( A_{1}, A_{2}, A_{3}, A_{4} \\) such that for any \\( x, y \\in S \\), there exists an \\( i \\in \\{1, 2, 3, 4\\} \\) where \\( x, y \\in A_{i} \\), determine the maximum possible value of the positive integer \\( N... | 999 |
[
{
"content": "Let \\( X \\sim \\mathcal{N}(0,1) \\) be a standard normal random variable. Compute \\( \\mathbb{E}[\\cos(X)] \\).",
"role": "user"
}
] | e^{-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... | 80J |
[
{
"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... | 5.55*10^5 m/s |
[
{
"content": "In a group, is it possible for two distinct elements to have equal squares, with neither being the identity element?",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( f \\) be a holomorphic function such that \\( c \\) is a zero of order \\( m \\) on \\( D_f \\). Evaluate \\( \\int _\\gamma \\frac{f'(z)}{f(z)}dz \\) where \\( \\gamma \\) is a circle centered at \\( c \\) contained in \\( D_f \\) and such that the other zeroes of \\( f \\) all lie outsid... | 2\pi i m |
[
{
"content": "Consider an oscillating random walk defined by the sequence of partial sums \\(S_n := X_1 + \\dots + X_n\\) with \\(S_0 := 0\\), where \\(X_1, X_2, \\dots\\) are independent and identically distributed random variables. The walk oscillates if it satisfies:\n\\[\n\\liminf_{n \\to \\infty} S_n = -\\... | No |
[
{
"content": "Evaluate the sum: $$ \\sum_{r=0}^n \\left[\\binom{n}{r}\\cdot\\sin rx \\cdot \\cos (n-r)x\\right] $$",
"role": "user"
}
] | 2^{n-1} \sin(nx) |
[
{
"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... | The phenoxide anion has a total of five resonance structures. The negative charge on oxygen is delocalized over the ortho and para positions of the benzene ring. |
[
{
"content": "Let T be a solid tetrahedron with four pairwise distinct non-coplanar vertices in three-dimensional Euclidean space. If p is any interior point of T and Q(p) is any plane containing p, does Q(p) always strictly separate two of the vertices of T? Answer yes or no.",
"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... | 0.362 |
[
{
"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... | 5.79 |
[
{
"content": "Find the radius of convergence of the Taylor series expansion of \\( \\frac{1}{\\cosh(z)} \\) centered at \\( z=0 \\). Use the formula for \\( \\cosh(z) \\) to determine the radius.",
"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... | 3.0e-4 N to the right |
[
{
"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... | -494 (kJ)/(mol) |
[
{
"content": "A point $P$ is randomly selected from the square region with vertices at $(\\pm 2, \\pm 2)$. What is the probability that $P$ is within one unit of the origin? Express your answer as a common fraction in terms of $\\pi$.",
"role": "user"
}
] | \frac{\pi}{16} |
[
{
"content": "In triangle $ABC$, $BC=115$, $AC=127$, and $AB=89$. Let $P$ be a point varying on the circumcircle of triangle $ABC$. Let $M$ and $N$ be the feet of the perpendiculars from $P$ to $AB$ and $AC$, respectively. Find the maximum value of the length of $MN$. Can this problem be solved using pure geome... | 115 |
[
{
"content": "In a plane, point C is located 300 meters due east of point B. A tower, not on the line connecting B and C, is observed from points B and C with vertical angles of 45 degrees and 60 degrees, respectively. From point D, which is 500 meters west of B, the tower is observed with a vertical angle of 3... | 300\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... | 0.0737 s |
[
{
"content": "Given the function \\( f(x) = \\begin{cases} g(x)\\cos\\frac{1}{x} & \\text{if } x \\neq 0 \\\\ 0 & \\text{if } x = 0 \\end{cases} \\), where \\( g \\) is an even function, differentiable at 0, and \\( g(0) = 0 \\), find \\( f'(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... | $351,818 |
[
{
"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 km/h |
[
{
"content": "Two identical rectangular crates are packed with cylindrical pipes, using different methods. Each pipe has diameter $10\\text{ cm}.$ A side view of the first four rows of each of the two different methods of packing is shown below.\n\n[asy]\ndraw(circle((1,1),1),black+linewidth(1));\ndraw(circle((... | 10 + 5\sqrt{3} |
[
{
"content": "Evaluate the limit: $$ \\lim_{n\\to\\infty}\\int_0^1x\\sin^nx\\,dx $$.",
"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... | 0.01 T in positive z direction |
[
{
"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... | 0.87g/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... | 76.5 cm^3 |
[
{
"content": "Calculate the value of the Riemann-zeta function at \\( s = 0 \\), i.e., find \\( \\zeta(0) \\).",
"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... | 19.3 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... | 140.8ms^-1 |
[
{
"content": "Given the function $f\\colon (0,\\infty)\\to\\mathbb R$ defined as $f(x)=x^n - n\\ln x + 1$ where $n\\neq 0$ and $n\\in\\mathbb{N}$, find the value of $a$ such that $f(x) = a$ for all $x \\in (0,1]$. Determine the value of $a$.",
"role": "user"
}
] | 2 |
[
{
"content": "Let $A$ be a non-singular square matrix of order $2$ such that \\(|A + |A|\\operatorname{adj}A| = 0\\), where \\(\\operatorname{adj}A\\) represents the adjugate of matrix \\(A\\), and \\(|A|\\) represents \\(\\det(A)\\). Evaluate \\(|A – |A|\\operatorname{adj}A|.\\)",
"role": "user"
}
] | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.96 grams |
[
{
"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... | 553 s^(-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... | 3.6138e+24 atoms |
[
{
"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... | $238,440 |
[
{
"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... | -$4394.11 |
[
{
"content": "Determine the residual spectrum of the operator $T_{\\alpha}$ when $(\\alpha_{n})$ is a constant sequence.",
"role": "user"
}
] | \emptyset |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.33 N |
[
{
"content": "Consider two vector spaces $X$ and $Y$ with dimensions six and four, respectively. Let $Z$ be a four-dimensional subspace of $Y$. Is it possible for every basis of $X$ to contain a basis of $Z$? 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... | 3.09e4 N |
[
{
"content": "Determine whether 0 can be a limit point of the set \\(\\{\\sum_{j=0}^{n-1}a_{j}e^{\\frac{2\\pi i j}{n}}: a_{0}, ..., a_{n-1} \\in \\mathbb{Z}\\}\\) in the complex plane for \\(n \\in \\mathbb{N}\\) and \\(n \\geq 2\\).",
"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... | 316 g |
[
{
"content": "Evaluate the sum \\( \\sum_{n=1}^{2019} \\lambda(n) \\left\\lfloor \\frac{2019}{n} \\right\\rfloor \\), where \\( \\lambda(n) = (-1)^{\\Omega(n)} \\) and \\( \\Omega(n) \\) is the number of prime factors of \\( n \\) counted with multiplicity. Use the properties of \\( \\lambda(n) \\) to find the ... | 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... | 1560Hz |
[
{
"content": "Let \\(A\\) be an infinite set in \\(\\mathbb{R}\\) with a single accumulation point in \\(A\\). Must \\(A\\) be compact?",
"role": "user"
}
] | No |
[
{
"content": "Suppose $h(x)$ is a function that satisfies the differential equation $h(x) - h''(x) = 0$. Define $k(x) = h^2(x) - h'^2(x)$. Given that $k(5) = 12$, find the value of $k(10)$. \\( \\text{Provide your answer in a box: } \\boxed{} \\)",
"role": "user"
}
] | 12 |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty}\\sum_{k=0}^n\\frac{^nC_k}{n^k(k+3)} \\).",
"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... | 68 photons/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... | Feb. 3, 2014: No Journal entry
Apr. 1, 2014: Debit Checking account $14,000,000, Credit Line of credit $14,000,000
Jun. 30, 2014: Debit Interest $245,000, Credit Interest payable $245,000
Jul. 1, 2014: Debit Interest payable $245,000, Debit Line of credit $14,000,000, Credit Checking account $14,245,000
Nov. 1, 2014: D... |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 257.27 moles |
[
{
"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... | 156800 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... | 0.72 m/s^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... | 6.89e-23 cm^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... | $15,124.08 |
[
{
"content": "Suppose we have a bounded domain $\\Omega \\subset \\mathbb{R}$ and a function $u$ such that the inequality $$\\|u'\\|_{L^{2}}^{2} + \\left( \\int_{\\Omega} u(x)~dx \\right)^{2} \\le C$$ holds, where $C$ is a constant. Is it necessarily true that $u \\in W^{1,2}(\\Omega)$?",
"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... | 0.0113 Ampere |
[
{
"content": "Find all polynomials \\( P(x) \\) with real coefficients such that \\( |P(x)| \\leq \\sum_{r=0}^{\\infty} |\\sin(x)|^r \\) for all \\( x \\in \\mathbb{R} \\).",
"role": "user"
}
] | P(x) = c |
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