Exam 10: Series and Taylor Polynomials

Determine the maximum error guaranteed by Taylor's Theorem with Remainder when the eighth-degree Taylor polynomial is used to approximate in the interval [0,1] centered at 0.Round your answer to five decimal places. ​ ​

​Use Newton's Method to approximate Round your answer to three decimal places. ​

​Find the radius of convergence of where ​

​Give an example of a sequence that converges to ​

A ball is dropped from a height of 14 feet,and on each rebound it rises to its preceding height.Write an expression for the height of the nth rebound.

Integrate the series for to find the power series for the function ​

A deposit of $800 is made each month in an account that earns 8.4% interest,compounded monthly.The balance in the account after n months is given by Find the balance after 20 years by computing the 240th term of the sequence.Round your answer to two decimal places. ​

​Write the first five terms of the sequence. ​ ​ ​

Write an expression for the ​nth term of the sequence , , , ,.... ​​

​A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions. ​ ​

​Find the third Taylor polynomial at for the given function. ​ ​ ​

​Find the radius of convergence of the power series. ​ ​ ​

​Determine the convergence or divergence of the following series. ​ ​

​Use a symbolic differentiation utility to find the fourth-degree Taylor polynomials (centred at zero). ​ ​​ ​

You are in a boat 2 miles from the nearest point on the coast (see figure).You are to go to a point Q,which is 3 miles down the coast and 1 mile inland.You can row at 4 miles per hour and walk at 5 miles per hour.Toward what point on the coast (from projection of initial position on the coast)should you row in order to reach point Q in the least time? Round your answer to three decimal places. ​ ​

​Find the sum of the convergent series. ​ ​ ​

​Determine the convergence or divergence of the p-series ​

Find the limit of the following sequence. ​ ​

​Use Newton´s Method to approximate the zero(s)of the function accurate to three decimal places. ​

​Use Newton´s Method to approximate the zero(s)of the function accurate to three decimal places. ​