On problems 3 and 4 find the radius of convergence and the interval of

# On problems 3 and 4 find the radius of convergence

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_________________________________________________________________________________________ On problems 3 and 4, find the radiusof convergence and the intervalof convergence. Show all work.3. 1127nnnnxnRadius = __________Interval = ______________________________________________________________________________________________________________4. 0232!nnnxnRadius = __________Interval = ____________________5. Let fbe the function given by sin33fxx, and let P xbe the third-degree Taylorpolynomial for fabout x= 0.(a) Find P x(b) Use the Lagrange error bound to show that 111222fP 2 . .
__________________________________________________________________________________________ 6. Find a power series for 14xfxxcentered at x= 0. Write the first four nonzero termsand the general term. 2 __________________________________________________________________________________________ 7. If fis a function such that sincos ,fxxxfind the coefficient of the 6xterm in the Taylor series for fxabout x= 0.8. The Maclaurin series for fxis given by 2462011...2!4!6!8!22 !nnnxxxxn.(a) Find 40 .(b) Determine whether f has a relative maximum, relative minimum, or neither at x= 0. Justify your answer.(c) Give the exact value for f(1) f __________________________________________________________________________________________ 9. The Maclaurin series for the function fis given by 12340248162...2341nnxxxxfxxn.(a) Write the first four nonzero terms and the general term for the Maclaurin series for fx(b) Use the Maclaurin series you found in (a) to approximate the value of 14f accurate to .01 .

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