8 questions

A Super Happy Fun Ball is dropped from a height of 16 feet and rebounds - of the distance from which it fell. a.) How many times will it bounce before its rebound is less than 1 foot? Enter an integer. It will bounce times before its rebound is less than 1 foot. b.) How far will the ball travel before it comes to rest on the ground? Express your answer as an integer or reduced fraction. It will travel feet before it comes to rest on the ground. 7 Consider the series ki k(k + 4) If it converges, find its sum. a.) First find the partial fraction decomposition of the magnitude of the kh term. 7 k(k + 4) b.) Then find the limit of the partial sums. 7 K 1 k(k + 4) Enter your answer for the sum as a reduced fraction. Hint: The series is a telescoping series. Write down its terms using the partial fraction decomposition until some terms cancel. Is the given series convergent? If so, compute the sum. If not, enter DNE (does not exist) for the sum. Use exact values. (-3)" - (-2)" 7 3 7n Question 13 Express 15. 20 as a ratio of two integers. Find the Maclaurin series of x e 7z 72 = 0 The Taylor series for f(a) = a3 at -1 is on(x + 1)" Question Help: Video Written Example Messag n= 0 Find the first few coefficients. Submit Question Co Question 5 S1 = Find the Maclaurin series of 2 C2 = C3 = CA = 0/1 pt 9 20 @ Deta We are interested in the first few Taylor Polynomials for the function f(z) = 7e + ge- centered at a = 0. To assist in the calculation of the Taylor linear function, T1 (), and the Taylor quadratic function, T2(), we need the following values: f(0) - f'(0) - f"(0) = Using this information, and modeling after the example in the text, what is the Taylor polynomial of degree one: Ti(x) = What is the Taylor polynomial of degree two: T2(I) =