The Maclaurin series expansion for cos(z) is: cos(x) = 1 - T² 2! +.... 4! 6! Starting with simplest version cos(z) = 1, add terms one at time to estimate cos(π/10). After each new term is added, compute the true and approximate percent relative errors. Add terms until value of approximate error estimation error falls bellow an error criterion conforming to two significant figures,

3 (b) Write power series of f(x) = about x = 0. 1- 4.r

FIND THE TAYWR SERIES FUR f (x) = 7 ABOUT x=-3 X4

(1) Solve for the power series representation of f(x)

Given f(x)=e^x+cos(2x)2.1 Find the Maclaurin series expansion. Show the first 8terms.

What are the first four terms of a Maclaurin series for  y(x) = (1+ x)-3 ?  Show each step of your working.

Solve for the following (Power Series)

A ball is dropped from a height of100 feet. Each time it hits the ground, it rebounds to 75% of its previous height. (a) Let Sn be the distance that the ball travels between the nth and the (n + 1)st bounce. Find a formula for Sn. (b) Let Tn be the time that the ball is in the air between the nth and the (n + 1)st bounce. Find a formula for Tn.

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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that R,(x) → 0.] Find the associated radius of convergence R. cos(3x) f(x) = 7 Step 1 The Maclaurin series formula is f(x) = f(0) + f'(0)x + 2! f"(0) x2 f''(0) ,3 1 f(4)(0) x4 + .... 3! 4! The function f(x) cos(3x) has the following derivatives. %3D 7 sin (3r) 3 sin(3r) f'(x) = 7 9 cos (3x) |-zcos(3e) f"(x) = 27 f''(x) = sin( 3r) 27 sin(3r) 81 f(4)(x) cos (3x) 81 - cos(3x) 7