instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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Let z(x) = 2*x**2. Let m(l) = -12386*l**2 + 68. Let k(a) = -1548*a**2 + 8. Let o(j) = 17*k(j) - 2*m(j). What is o(z(b))?\n | -6176*b**4\n | ibivibiv/math_instruct | |
Let k(w) = w**3 - 330*w**2 + 5113*w - 1408. Calculate k(16).\n | 16\n | ibivibiv/math_instruct | |
Is 39050631155 a prime number?\n | False\n | ibivibiv/math_instruct | |
Is 0.02 less than or equal to 65?\n | True\n | ibivibiv/math_instruct | |
Rearrange (17*k - 67 - 31*k + 13*k + (3 - 25 - 21)*(-2*k - 2 + 2))*(0 + k**2 + 0) to the form c*k**2 + t*k**3 + b + l*k and give c.\n | -67\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 948 and 1027.\n | 12324\n | ibivibiv/math_instruct | |
Let m(c) = 2*c**2 + 44*c + 99. What is m(-23)?\n | 145\n | ibivibiv/math_instruct | |
Let k be 2*5/10*-22. Let v be (-17)/(-2) - 11/k. Solve -4*z = c - 2*z - v, -5*c - 3 = -2*z for c.\n | 1\n | ibivibiv/math_instruct | |
Let m = -2.51 + 2.81. Let b(j) = j**3 + 9*j**2 + 13*j - 2. Let v be b(-7). Sort v, m, 1/5 in descending order.\n | v, m, 1/5\n | ibivibiv/math_instruct | |
Subtract 5 from -604297.\n | -604302\n | ibivibiv/math_instruct | |
915+-20361569.504\n | -20360654.504\n | ibivibiv/math_instruct | |
Find the second derivative of -214216*a**2*s**2 + a*s**2 + a*s + 123702*a wrt a.\n | -428432*s**2\n | ibivibiv/math_instruct | |
List the prime factors of 18113349.\n | 3, 41, 147263\n | ibivibiv/math_instruct | |
Let q be (-9 - (-8 + 7))/(-4). Solve -104*y + 105*y = q for y.\n | 2\n | ibivibiv/math_instruct | |
Let l = -4.92 + 5. Let p = -0.11905 + 0.03893. Let m = l + p. What is m rounded to five dps?\n | -0.00012\n | ibivibiv/math_instruct | |
Let y = -4 - -7. Suppose 3*b = 2*s - 20, 3*s + y*b - 50 = -2*s. Solve s = -2*g + 7*g for g.\n | 2\n | ibivibiv/math_instruct | |
Is 75 a multiple of 60?\n | False\n | ibivibiv/math_instruct | |
Let g(t) be the first derivative of -t**4/2 - 5*t**3/3 + t**2/2 + 4*t - 1. Let h be g(-4). Let m(x) = 48 - h + x**2. Let d(c) = 4*c. Determine m(d(v)).\n | 16*v**2\n | ibivibiv/math_instruct | |
What is the second derivative of 5*c*s**5 + 5*c*s**2 - 97*c - 600*s**5 - 258*s wrt s?\n | 100*c*s**3 + 10*c - 12000*s**3\n | ibivibiv/math_instruct | |
Let i(u) = 18*u - 1. Let y be 8 + 1/((-5)/15). Let m be i(y). Suppose 5*w + m = 284. List the prime factors of w.\n | 3, 13\n | ibivibiv/math_instruct | |
Put together -5298108 and 47842222.\n | 42544114\n | ibivibiv/math_instruct | |
What is prob of sequence rni when three letters picked without replacement from {m: 5, r: 9, n: 1, i: 3}?\n | 3/544\n | ibivibiv/math_instruct | |
Solve 0 = -21*t - 98*t - 77*t for t.\n | 0\n | ibivibiv/math_instruct | |
What is 3.396434 millilitres in litres?\n | 0.003396434\n | ibivibiv/math_instruct | |
What is the hundreds digit of 72277?\n | 2\n | ibivibiv/math_instruct | |
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"Home > Taylor Series > Taylor Series Error Estimation
Taylor Series Error Estimation
Contents
Example What is the minimum number of terms of the series one needs to be sure to be within of the true sum? However, it holds a... | The topic at hand is the error estimation of Taylor series, specifically focusing on the integral form of the remainder. To understand this concept fully, let us begin by reviewing some fundamental ideas about Taylor series.
A Taylor series is a representation of a function as an infinite polynomial centered around a... | ibivibiv/math_instruct | |
Calculate the highest common divisor of 52459866 and 270.\n | 54\n | ibivibiv/math_instruct | |
Is 0 + 2 + (205 - 2) composite?\n | True\n | ibivibiv/math_instruct | |
Calculate prob of sequence wwzs when four letters picked without replacement from wzwwszw.\n | 1/35\n | ibivibiv/math_instruct | |
Let u = -3 + -5. Let m = 45 - 47. What is the biggest value in 0.1, m, u?\n | 0.1\n | ibivibiv/math_instruct | |
What is the remainder when 12 is divided by -4*6*(-3)/24?\n | 0\n | ibivibiv/math_instruct | |
7503503.4+-2.57\n | 7503500.83\n | ibivibiv/math_instruct | |
What is next in -246648, -246553, -246394, -246171?\n | -245884\n | ibivibiv/math_instruct | |
What is prob of sequence cnhc when four letters picked without replacement from {h: 4, n: 7, c: 3}?\n | 1/143\n | ibivibiv/math_instruct | |
Let i(h) = 3 + 2 - 6 + 4*h. Let v(r) = 16*r - 5. Let m(z) = 9*i(z) - 2*v(z). What are the prime factors of m(2)?\n | 3\n | ibivibiv/math_instruct | |
0.5 times 0.404\n | 0.202\n | ibivibiv/math_instruct | |
Which is greater: 1/1382 or -1?\n | 1/1382\n | ibivibiv/math_instruct | |
Suppose 0 = 3*r - 3*p + 39, 7 = r - 5*p. Sort -2, 1, -3, r in increasing order.\n | r, -3, -2, 1\n | ibivibiv/math_instruct | |
Let t(w) = w**2 + 10*w - 8. Let q be t(-11). Let f be (-28)/(-7) - 2*1. What is the derivative of q*o**2 - f*o**2 + 1 + 2 wrt o?\n | 2*o\n | ibivibiv/math_instruct | |
Suppose 403*b = 405*b - 20. Let d(u) = -u**2 + 20*u - 68. Let j be d(b). Is 33 at most j?\n | False\n | ibivibiv/math_instruct | |
Let u = -349 - -192. Let i = u - -154. Let f = -12 + 7. Sort f, i, 4 in descending order.\n | 4, i, f\n | ibivibiv/math_instruct | |
Let f(y) = -y**3 + 8*y**2 + 10*y - 7. Let b be f(9). Suppose 3*d - 5 = 2*d. Suppose 3*m + 2*m - 70 = d*u, -b*u = -8. Is 9 a factor of m?\n | True\n | ibivibiv/math_instruct | |
Rearrange (5 - c**2 - 5)*(1 - 4 + 1)*(2 - 5 + 0) to the form s + y*c + h*c**2 and give h.\n | -6\n | ibivibiv/math_instruct | |
Which is greater: 1670 or 0?\n | 1670\n | ibivibiv/math_instruct | |
What is the closest to 20/11 in -2/9, 1/1042, 5, -0.1, -2?\n | 1/1042\n | ibivibiv/math_instruct | |
Let n(f) = 2*f + 5 - 4*f - 3 + 3*f. Suppose -3*m - m = 4*u - 4, -5*m + 8 = 2*u. Let d be n(m). Solve -5*s + 5 = 5*q, -q + 5*q - 2*s - d = 0 for q.\n | 1\n | ibivibiv/math_instruct | |
Let r be 3 + 3 - ((-4)/14 - 111786/(-17577)). Which is the fourth biggest value? (a) r (b) -1/4 (c) 50 (d) 2\n | b\n | ibivibiv/math_instruct | |
What is 12131 to the power of 1/3, to the nearest integer?\n | 23\n | ibivibiv/math_instruct | |
Calculate the remainder when 17136472 is divided by 202.\n | 4\n | ibivibiv/math_instruct | |
What is 601069204 to the power of 1/3, to the nearest integer?\n | 844\n | ibivibiv/math_instruct | |
Let b(w) be the second derivative of 0*w**5 + 0*w**4 - 12*w + 0 - 3/10*w**6 + 1/3*w**3 + 0*w**2. What is the second derivative of b(y) wrt y?\n | -108*y**2\n | ibivibiv/math_instruct | |
What is the result of the following expression?
26.335 + (3.644 - -48.763) | 78.7420 | ibivibiv/math_instruct | |
Three letters picked without replacement from ryiriiryjyy. What is prob of picking 1 i and 2 y?\n | 6/55\n | ibivibiv/math_instruct | |
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"# How can I derive the function curve from a histogram of observed data
I'm analysing some datasets that produce heavy tailed data when plotted as a histogram. My initial goal was to attempt to fit a known distribution to my... | To begin, let's discuss the process of deriving a function curve from a histogram of observed data. A histogram is a type of graph used to display the frequency distribution of continuous numerical data. It organizes data into intervals called bins, which are displayed along the horizontal axis (x), while the vertical... | ibivibiv/math_instruct | |
Rearrange 11791*x + 40 + 4138*x + 17670*x - 40 to b*x + d and give b.\n | 33599\n | ibivibiv/math_instruct | |
Let u(n) = 9*n - 13. Suppose 2*x = 4*m - 6, -m - 2*m + 7 = -x. Let i be u(m). Solve -i*b + 18*b - 15 = 0 for b.\n | -3\n | ibivibiv/math_instruct | |
Convert 4 (base 15) to base 2.\n | 100\n | ibivibiv/math_instruct | |
Suppose 0 = 14*b - 207 - 633. Let c be -6 + (0 - b/(-6)). Solve c*u - 31 = -3*r, 3*u - 2*r + 1 = 3 for u.\n | 4\n | ibivibiv/math_instruct | |
Is 453775279 a multiple of 278?\n | False\n | ibivibiv/math_instruct | |
b"What is the nth term of 37916357, 37916343, 37916329, 37916315, 37916301?\n" | -14*n + 37916371\n | ibivibiv/math_instruct | |
Calculate 196861686 divided by 3394167.\n | 58\n | ibivibiv/math_instruct | |
Let o(u) = -u**2. Let i(f) = f**2 + f**2 + f**2. Let g be (5 - (-36)/(-6))*(14 + 0). Suppose 2*b + 3*b + 20 = 0. Calculate b*i(s) + g*o(s).\n | 2*s**2\n | ibivibiv/math_instruct | |
Is 2/(-2)*(18 + -4679) composite?\n | True\n | ibivibiv/math_instruct | |
Let v = 6 - 0. Let b(j) = j**3 - 7*j**2 + 8*j - 9. Let z be b(v). Suppose z*g + 9 - 24 = 0. What are the prime factors of g?\n | 5\n | ibivibiv/math_instruct | |
Three letters picked without replacement from issitss. What is prob of picking 1 s and 2 i?\n | 4/35\n | ibivibiv/math_instruct | |
Four letters picked without replacement from vvrvvvvvrvvv. What is prob of picking 4 v?\n | 14/33\n | ibivibiv/math_instruct | |
How many minutes are there in 10/9 of a week?\n | 11200\n | ibivibiv/math_instruct | |
What is the closest to -0.03 in -1, -2, -0.1, 0?\n | 0\n | ibivibiv/math_instruct | |
What is the units digit of 2253762?\n | 2\n | ibivibiv/math_instruct | |
Simplify ((sqrt(128) - (3 + sqrt(128))) + -5)*-2.\n | 16\n | ibivibiv/math_instruct | |
Suppose 20*j - 968 = 9*j. Suppose -3*g = -2*m - 236, -g - 2*m = 2*m - j. What is the tens digit of g?\n | 8\n | ibivibiv/math_instruct | |
Let v(x) = 4*x - x + 3 + 3 + 1. Calculate the remainder when v(5) is divided by 8.\n | 6\n | ibivibiv/math_instruct | |
What is 1606/165 - 10 - (8 + (-2793)/180)?\n | 29/4\n | ibivibiv/math_instruct | |
Suppose 4*r - 144 = -2*f, 0*r + 4*f - 140 = -4*r. What is the remainder when 102 is divided by r?\n | 28\n | ibivibiv/math_instruct | |
Simplify (h**(-9)/(h*(h/(h/((h**(1/3)*h)/h)))/h))/(h**(3/5)*h**(2/7)) assuming h is positive.\n | h**(-1073/105)\n | ibivibiv/math_instruct | |
Find the second derivative of 2071*k**3*n**5 + 187*k**3*n**2 - 732*k**3*n + 102*k**2 + 2*n wrt n.\n | 41420*k**3*n**3 + 374*k**3\n | ibivibiv/math_instruct | |
Simplify (sqrt(78)/(sqrt(24)/sqrt(4)*5) - (sqrt(1573) - (5 + sqrt(1573) + 0 + sqrt(1573))))**2.\n | 112*sqrt(13) + 41393/25\n | ibivibiv/math_instruct | |
b"What is the vth term of -336, -612, -888, -1164, -1440?\n" | -276*v - 60\n | ibivibiv/math_instruct | |
Does 36 divide 2988?\n | True\n | ibivibiv/math_instruct | |
What is next in -3, 23, 49, 75, 101, 127?\n | 153\n | ibivibiv/math_instruct | |
Work out -1743376826724 - 3.5.\n | -1743376826727.5\n | ibivibiv/math_instruct | |
Which is the sixth biggest value? (a) -11 (b) 0.1 (c) -1/4 (d) -3/4 (e) -2/9 (f) 33\n | a\n | ibivibiv/math_instruct | |
What is prob of sequence nbn when three letters picked without replacement from {n: 2, b: 9}?\n | 1/55\n | ibivibiv/math_instruct | |
Let m = -35 - -38. Suppose -m*s + s = 30. Is (-5710)/s*3/2 composite?\n | False\n | ibivibiv/math_instruct | |
Calculate -27438 divided by -55.\n | 27438/55\n | ibivibiv/math_instruct | |
Solve d - 3*p - 2 = 0, -73*p = 5*d - 68*p - 30 for d.\n | 5\n | ibivibiv/math_instruct | |
Simplify d**15*d*d**(2/13)*d*(d**6*d)/(d*d**6*d) assuming d is positive.\n | d**(210/13)\n | ibivibiv/math_instruct | |
Collect the terms in -13675422360 + g**2 + 13675422360.\n | g**2\n | ibivibiv/math_instruct | |
What is the common denominator of -83/2 and 97/638?\n | 638\n | ibivibiv/math_instruct | |
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"If you want to make money online : Register now
# [Solved]: what is the time complexity for an algorithm that operations to complete grows by 4 when doubling the input length?
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Problem Detail:
I'm working on an algorith... | When analyzing algorithms, computer scientists often seek to understand how their running time increases as the size of the input changes. This analysis allows them to compare different algorithms and choose the most efficient one for solving a particular problem. The concept of time complexity provides a way to quant... | ibivibiv/math_instruct | |
Which is smaller: -81623 or -81618?\n | -81623\n | ibivibiv/math_instruct | |
Convert 0.953238 weeks to days.\n | 6.672666\n | ibivibiv/math_instruct | |
What are the prime factors of 199937390?\n | 2, 5, 23, 869293\n | ibivibiv/math_instruct | |
Calculate 5796311 divided by -19.\n | -305069\n | ibivibiv/math_instruct | |
Solve -2*l = 3*i + 19, 1523 = 3*l + i + 1534 for l.\n | -2\n | ibivibiv/math_instruct | |
What is the thousands digit of 3958342?\n | 8\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 22 and 58.\n | 638\n | ibivibiv/math_instruct | |
Let v = 4657998.052358239 - 104.043458239. Let r = v - 4657672. Let m = -222 + r. Round m to three dps.\n | 0.009\n | ibivibiv/math_instruct | |
Calculate the remainder when 549914 is divided by 274957.\n | 0\n | ibivibiv/math_instruct | |
Suppose 47342402 = 4*g - 6*b + 7*b, -4*g + 47342416 = 8*b. What is g rounded to the nearest one million?\n | 12000000\n | ibivibiv/math_instruct |
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