Pblem 1:
(a) Calculate s4 for the series given below and determine an upper bound for how far s4 is from the exact valueS of the infinite series.
(b) Use s4 to find lower and upper bounds on the value of S so that {lower bound} < S < {upper bound}.
(b) Since it is not known whether the error in part (a) makes s4 greater than S or less than S, the error can be used with s4 to compute lower and upper bonds on S:
Problem 2:
Show that:
Problem 3:
Use the substitution method and a known power series to find the power series for the given function:
Problem 4:
Calculate the first several terms of the Maclaurin series for the given function
Problem 5:
Calculate the Taylor Polynomials P0, P1, P2, P3, and P4 for the given function centered at the given value of c. Then graph the function and the Taylor polynomials on the given interval.
