Pblem 1:

(a) Calculate

*s*_{4}for the series given below and determine an upper bound for how far*s*_{4}is from the exact value*S*of the infinite series.(b) Use

*s*_{4}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

*s*_{4}greater than*S*or less than*S*, the error can be used with*s*_{4}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

*P*_{0},*P*_{1},*P*_{2},*P*_{3}, and*P*_{4}for the given function centered at the given value of*c*. Then graph the function and the Taylor polynomials on the given interval.