Sin(x) can be expressed by Taylor series as below o (-1)"x2n+1 x3 = x x5 x7 sin(x) = En=0 (2n+1)! 3! 5! 7! Write a F90 program to calculate sin(x) taking appropriate number of terms.

Q: For f(x) = 3 + 7x - 19(x^2) + 2(x^4) find the maclaurin series (Taylor series about x =0) Please do…

A: The Solution is given below:

Q: [xus (2) x+10) xuIsx(p) x(1) (k)1 ×sinx (1x [x][a] (k) 1 x (m)xcosx

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Q: Q5: a\. Let f(x) = x³ - 3x² -1, x ≥ 2. State and prove the theorem of derivative of inverse…

A: Here , f(x) = x3-3x2-1 We find required value.

Q: The Fourier series of the function is given by f(x) ~ co- where CO = Cn = and f(x) = bn. = = =0 n=…

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Q: 3. Find Taylor series for tan-1x about x =1 .

A: We find the Taylor series for tan-1x about x=1.

Q: Compute the Fourier series for z+z on (-=,=).

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Q: For any positive integer n, prove that summation d divides n t(d)^(3) = ( summation d divides n t(d)…

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Q: Find the coefficients of the power series c0, c1, c2, c3, c4 for f(x)=ln(1-x^2)?

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Q: Find the Fourier series of, - 2 < x< -1 f(x) = }-2 -1< x<1 1< x< 2

A: We have to find the Fourier series of the given function.

Q: Find the Taylor series for f(x) = 6/(1 − 2x)^2

A: The given function is fx=61-2x2. Obtain the Taylor series for fx=61-2x2 centered at x=0 as follows.…

Q: Consider the following sequences n G In (1+n) (ii) e^/ (n²+1), (iii) √√n²+ √n²+2n -n. Which of the…

A: Let {an} be a sequence of real numbers If an≤an+1 ∀ n∈N then the sequence an is called monotonically…

Q: find the series of cosx4 and (cosx)4

A: The series for cosx is cosx=1-x22!+x44!-x66!+...

Q: The sequence {xk} has the Z transform 3z(z-1) z): Find {xk} z3-2z2-4z+8

A: According to the given information, it is required to find the z transform of the given function.

Q: ο Σπo (-6)" x2n+3 Ο Σo 6" x2n+3 100 ο Σο (-6)" man Ο Σπο (-6)" an Ο Σπο 6 x 2n Find a power series…

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Q: Question 5 (Show your work!) Find the coefficients of 1. x10 in (x + (1/x))122. 2. xk in (x² –…

A: (x+(1/x))122 general term Tr+1 =Crnxn-r(1/x)r  =Cr122x122-2r to find coefficients of x10 compare…

Q: Find Fourier series for f (x) = 2x + 1

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Q: 1) Find the Taylor Series for sin(x)

A: Since you have posted multiple questions, according to our guidelines we have done first question…

Q: 1. A power series is a series of the form and cn's are where x is a 2. The power series can be…

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Q: (- 1)^2n- x2n-1 is 2 n = 0 (- 1)"x2n The derivative of the series 2 n= 0 2" 2" O True

A: We have to find the derivative of the given power series and need to verify whether the given…

Q: Expand ?(x) = x2, −1 < x < 1 into an appropriate cosine or sine series

A: Given,fx=x2   , -1&lt;x&lt;1

Q: Express f(x) = n + x_for -<x<n as a Fourier series.

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Q: Let f be the function defined for - ≤ x ≤ π by 1 0 f(x) if - π/2 ≤ x ≤ π/2 otherwise and then…

A: given function f defined for -π≤x≤π by fx=1if -π2≤x≤π20otherwise and then extended to be 2π periodic…

Q: Civen that the Maclurin Series f Cosine function is (17) in (-1) C 2n e Let f lx) = x cos(x?).Find…

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Q: 4 sinx+=sin3x +=sin5x+..... and that when x=, 1 1 6. If it is given that the Fourier Series is f(x)=…

A: The Fourier Series is

Q: expand the function f(x) = sin(x) / (coshx +2) in a taylor series around the origin going up to x^3.…

A: Taylor series of function f(x) around x=a is defined as:

Q: 1. A power series is a series of the form and Cn's are where x is a

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: What is the 7th term in the Taylor series for f(x) = 5e5* taken about x 7th term = 7-6-5-4-3-2-1-36…

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Q: specified terms in each the fo

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Q: f(x) = (x² + + 6) cos(4x) 3 х

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Q: Write in detail differece between Fourier transform and Fourier series with formula and example.Also…

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Q: Expressf (x)=x asa Fourier series in (-rt,7)

A: We can use the below formula to find the Fourier series for f(x) = x.