This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Chapter 9 Practice Test A
1. 2. Express the repeating decimal 0. 621 as a geometric series and find its sum. Given that 1 for 3. 1 x x2 x3 … x
n is a power series representation x3 . x2 sin 2 x , find a power series representation for 1 x 1 Find the Taylor polynomial of order 3 generated by f x x at 4. . 4 Let f be a function that has derivatives of all orders for all real numbers. Assume f 0 5, f 0 3, f 0 8, and f 0 24. Write the third order Taylor polynomial for f at x 0 and use it to approximate f 0.4 . The Maclaurin series for f x 1 a b c 2x 3 x2 2 4 x3 6 … n n x . Write the Maclaurin series for g x . is 1 xn …. 5. Find f 0 . Let g x xf
x Let h x
0 f t dt. Write the Maclaurin series for h x . ln 1 x2 at x 0 6. 7. Find the Taylor polynomial of order 4 for f x and use it to approximate f 0.3 . The polynomial 1 on the interval 7x 0.01 21 x2 is used to approximate f x 1 x7 x 0.01. Find the maximum absolute error. 8. Determine the convergence or divergence of each series. Identify the test or tests you use. a
n 2 2n n 1 3n b
n 1 n2 3n n 4 c
n 1 1 1 2n 3n 9. Determine whether each series converges absolutely, converges conditionally, or diverges.
2 2n n1 n3 10. Find the radius of convergence of each power series. n 1 a 1 n3 n b cos n
n 1 c 1 n n3 ln n 2 a
n 0 4x 7n n b
n 1 3x n 4 5n n 11. Find the interval of convergence of the series
n 0 4x 8n 3 3n and, within this interval, the sum of the series as a function of x. 12. Determine all values of x for which the series
n 1 2n sinn x n2 converges. 13. Find the interval of convergence of the series
n 1 3n n x 2 2 n . 2n 14. Use the integral test to determine whether the following series
1 converges or diverges :
n 1 en n2 15. Use the Direct Comparison Test to determine whether the following series converges or diverges :
n 1 tan n 1 n n 1 16. Using what you know about the function 1 representation for the function fx , find a power series x 2 4 3x ...
View Full Document