-{1 f(x) -2

Q: f(x) x² + 3

A: Find the power series expansion of  f(x)

Q: find the lourent's series for function f(z)= ((z^2)-3z+2)^(-1) 0</z-1|<1

A:

Q: Show that the series sin2x+sin4x+sin6x+... converges to tan2x if x≠(π/2)+nπ

A: Here I am attaching image so that you understand each and every step.

Q: Find a Maclaurin series for f(x). (Use for 1·3· 5·.. (2n – 3).) 2"n!(2n-1) f(x) V1 + t3 dt f(x) = x…

A: given fx=∫0x1+t3dt to find the maclaurin series

Q: 5. Determine the half range Fourier cosine series for -{- f(x)= 7-X

A:

Q: f(z) = (2+2)(2+

A:

Q: show why g(x) cannot be represented by a MacLauren series. g(x) = { 0 if x < 0 , x^ 3 if x ≥ 0

A:

Q: What is the maclaurin series for f(x)= 1/x-1 ?

A: Given, F(x)=1x-1we have to find the maclaurin series of the given function.

Q: What is the power series for f(x)= 2/1+7x ?

A: we have been given the function  f(x)=21+7x

Q: Let a„(x) = (n + 1)²™”, and define f(x) = an(x). n=0 a) Evaluate the following quantities: lim h(x)…

A: We have;

Q: (i) The area of a triangle is (basexheight). (ii) Compute the areas A1, A2, etc..., find a pattern…

A: We know, I = ∫04f(x)dx=A1+A2+A3+.....

Q: Match each function with its power series representation. Functions: Power Series: Function 1: 2 1…

A:

Q: (x-1)" Which are the values of for which the series n=1 n A. 0SX<2 O B. -1<x<1 O C.0<x<2 O D. -1sxs1

A:

Q: f (x) = cos(2\x) Find the MacLaurin Series for = Cos(2.

A:

Q: Find the taylor until 4 non zero terms for series a) f(x) = In(x) at X= 3

A:

Q: The first derivative of the power series 9 9x2 9x3 9x4 f(x)=9+ .. is 1! 2! 3! 4! O -9 f(x) O f(x)…

A:

Q: It can be shown that the series 6·(-2)" -x²" converges to f (x)= 1+2x? 7. on the interval n=0 1 1…

A:

Q: If xo is in the interval of convergence of a power series En=1 an(x – c)" that represents a function…

A: We can answer first question as per the honor policy. Please resubmit the other question as well to…

Q: Find the Fourier series of the function if -4 < x< 0 X f(x) S(x + 8) = f(x) if 0 <x< 4

A:

Q: Find the binomial series for f(x)= (1 +x)²" 2'

A:

Q: Write power series of f(x) = 3 about x = 0. %3D 1- 4.r

A:

Q: te the Taylor series for f(x) = S

A: