17.The coefficient of the x' term in the Maclaurin polynomial for sin(2x) is(A) 0(B) 0.0083333(C) 0.016667(D) 0.26667Given f(3) = 6, f'(3)= 8, f"(3) =11, and that all other higher order derivatives off(x) are zero at x = 3, and assuming the function and all its derivatives exist and arecontinuous between x= 3 and x= 7, the value of f(7) is18.(A) 38.000(B) 79.500(C) 126.00(D) 331.50Given that y(x) is the solution todx=y +2, y(0) = 3 the value of y(0.2) from a19.second order Taylor polynomial written around x =0 is(A) 4.400(B) 8.800(C) 24.46(D) 29.00The series (-1)"-20.,4" is a Maclaurin series for the following function(2n)!(A) cos(x)(B) cos(2x)(C) sin(x)(D) sin(2x)21.The functiondtis called the error function. It is used in the field of probability and cannot becalculated exactly for finite values of x. However, one can expand the integrand as aPage 4 of 5Taylor polynomial and conduct integration. The approximate value of erf (2.0) usingthe first three terms of the Taylor series around t = 0 is(A) -0.75225(B) 0.99532(C) 1.5330(D) 28586 22.Using the remainder of Maclaurin polynomial of n* order for f(x) defined asR.(r)= ,-glas(c), n20, 0sesx(n +1)the least order of the Maclaurin polynomial required to get an absolute true error of atmost 10* in the calculation of sin(0.1) is (do not use the exact value of sin(0.1) orcos(0.1) to find the answer, but the knowledge that |sin(x)| S1 and | cos(x) |S 1).(A) 3(В) 5(C) 7(D) 923.The Maclaurin series expansion for cos x iscos(x) =1-2!4!6!Starting with the simplest version, cos x = 1, add terms one at a time to estimatecos(z/3). After each new term is added, compute the true and approximate percentrelative errors. Use your pocket calculator to detemine the true value. Add termsuntil the absolute value of the approximate error estimate falls below an errorcriterion conforming to two significant figures.24.Perform the same computation as in Prob. 23, but use the Maclaurin series expansionfor the sin x to estimate sin(n/3).sin(x) =x-+3!5!7!

Question

17.The coefficient of the x' term in the Maclaurin polynomial for sin(2x) is(A) 0(B) 0.0083333(C) 0.016667(D) 0.26667Given f(3) = 6, f'(3)= 8, f&#34;(3) =11, and that all other higher order derivatives off(x) are zero at x = 3, and assuming the function and all its derivatives exist and arecontinuous between x= 3 and x= 7, the value of f(7) is18.(A) 38.000(B) 79.500(C) 126.00(D) 331.50Given that y(x) is the solution todx=y +2, y(0) = 3 the value of y(0.2) from a19.second order Taylor polynomial written around x =0 is(A) 4.400(B) 8.800(C) 24.46(D) 29.00The series (-1)&#34;-20.,4&#34; is a Maclaurin series for the following function(2n)!(A) cos(x)(B) cos(2x)(C) sin(x)(D) sin(2x)21.The functiondtis called the error function. It is used in the field of probability and cannot becalculated exactly for finite values of x. However, one can expand the integrand as aPage 4 of 5Taylor polynomial and conduct integration. The approximate value of erf (2.0) usingthe first three terms of the Taylor series around t = 0 is(A) -0.75225(B) 0.99532(C) 1.5330(D) 28586 22.Using the remainder of Maclaurin polynomial of n* order for f(x) defined asR.(r)= ,-glas(c), n20, 0sesx(n +1)the least order of the Maclaurin polynomial required to get an absolute true error of atmost 10* in the calculation of sin(0.1) is (do not use the exact value of sin(0.1) orcos(0.1) to find the answer, but the knowledge that |sin(x)| S1 and | cos(x) |S 1).(A) 3(В) 5(C) 7(D) 923.The Maclaurin series expansion for cos x iscos(x) =1-2!4!6!Starting with the simplest version, cos x = 1, add terms one at a time to estimatecos(z/3). After each new term is added, compute the true and approximate percentrelative errors. Use your pocket calculator to detemine the true value. Add termsuntil the absolute value of the approximate error estimate falls below an errorcriterion conforming to two significant figures.24.Perform the same computation as in Prob. 23, but use the Maclaurin series expansionfor the sin x to estimate sin(n/3).sin(x) =x-+3!5!7!

Accepted Answer

Answered: Image /qna-images/answer/7507b1f0-a039-4f69-bae5-a8a8d40ca406.jpg

The coefficient of the r term in the Maclaurin polynomial for sin(2x) is (A) 0 (B) 0.0083333 (C) 0.016667 (D) 0.26667 17.