AP Calculus BC

AP Calculus BC Review for Quiz Determining convergence of geometric series Creating a power series Finding a Taylor Series sum expression

Question 1 For the series below: Write the first 4 terms of the series, then find the sum that the series converges to.

Solution Q1 • 5 + 5/4 + 5/16 + 5/64 converges to 20/3

Question 2 Find the power series expression for Then use your result to find a power series representation for

Solution Q2 And

Question 3 Determine the fourth order Taylor series and the summation equation for f(x) = 1/x when the center is at x = -1

Solution Q3 = - 1 – (x+1) - -

Question 4 • Tell whether each converges or diverges, if it converges give its sum a. • + . . . . . • x - + - + . . . .

Q4 key • Converges to 6 • Converges to 2/3 (r = -1/2) • Diverges • Sin x

Question 5 Find the interval of convergence and the function of x represented by the geometric series

Q5 key • The interval of convergence is – 1 < x < 3 • And f(x) =

Question 6 Find the interval of convergence and the function of x represented by the geometric series

Q6 key • f(x) = • And interval of convergence is (1,5)

Question 7 Find first four terms of the Taylor polynomial for y =

Q7 key = 1 + (2x) +

Question 8 Find the 5th partial sum and also what the series converges to.

Q8 Key 5th partial sum is = = 13.02469 Converges to: 15