Find the Maclaurin series of the following functions by making suitable substitutions nto one of the Maclaurin series for e", sin(x),,. 1 (i) е *, (i) sin(2г»), (ійі) 1+ x³ °

Q: The series 33n 23n–2 is a geometric series. (1) What is its initial term a ? a = (ii) What is the…

A: a) To find the initial term we put n=1 Answer(a): 13.5

Q: Find the Laurent's Series for 3 2 sinz fIZ)-Ze f(z) = (조-Ty e Hur felle

A:

Q: #3. Prove that 2 = tan [ = log (T_-_ iz)

A: To Prove:z=tan1ilog1+iz1-iz12.

Q: Expand f(x)=sin(x) on the  interval (0,pi) [Fouries Series] a) in consine series b) in sine series

A: PART A: Concept Used: The half range cosine series of the function fx is given by  fx=a0+∑ancosnπxl…

Q: How to write sin(x)cos(3x) in power series

A: We need to write sin(x)cos(3x) in the power series. Taylor series of function fx at a is defined as:…

Q: Differentiate the Maclaurin series of e", sin(x) and cos(x) to double-check that (e")' = e®, that…

A: We will use well known maclaurin series in this question.

Q: Approximate cos(0.2) to five decimal-place accuracy using the MacLaurin series for cos(x). cos(0.2)~

A: MacLaurin series of cosx is  cosx = 1- x2/2! + x4/4! - x6/6! + ......... We have to find the value…

Q: sin(x) Find the Maclaurin series of

A:

Q: 4. Obtain (a) the half-range cosine series and f(t)= (b) the half-range sine series for the function…

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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: 6) Find a power series for tan(X)². Please show your steps.

A: