Chapter9A - Chapter 9 Practice Test A 1. 2. Express the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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

Ask a homework question - tutors are online