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1. [-/1 Points] DETAILS LARCALC12 9.1.041. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHI Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) a = 6110. [-/2 Points] DETAILS LARCALC12 9.6.044.MI. MY NOTES ASK YOUR TEACHER Consider the following series. E -50 3n 2n + 1 n = 1 Using the Root Test, find the following limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim V lal = Determine the convergence or divergence of the series. If the Root Test is inconclusive, determine the convergence or divergence of the series using other methods. O converges diverges11. [-/1 Points] DETAILS LARCALC12 9.7.028. Find the nth Taylor polynomial for the function, centered at c. f ( x ) = 1 n = 4, c= 5 PA(X) =12. [-/1 Points] DETAILS LARCALC12 9.7.031. Find the oth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c=3 PA(X) =13. [-/1 Points] DETAILS LARCALC1Z 9.7.040. MY NOTES | ASK YOUR Approximate the function at the given value of x, using the Maclaurin polynomial of degree n = 4. (Round your answer to four decimal places.) f(X) x2e xzx3+x 2 X 1 4 14. [-/1 Points] DETAILS LARCALC12 9.7.051. MY NOTES ASK YOUR TEACHER P Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = sin(x), approximate f(0.5) 17. [-/1 Points] DETAILS LARCALC12 9.8.012.MI. MY NOTES ASK YOUR TE Find the radius of convergence of the power series. (If you need to use co or -co, enter INFINITY or -INFINITY, respectively.) (-1)" x n = 0 8718. [-/1 Points] DETAILS LARCALC12 9.8.013. MY NOTES ASK Find the radius of convergence of the power series. (If you need to use co or -co, enter INFINITY or -INFINITY, respectively.) x5n n = 0 (5n)!19. [-12 Points] DETAILS LARCALC1 2 9.9.004. Find a geometric power series for the function, centered at 0, by the following methods. 2 3+x l'(X) = (a) by first writing f(x) in the form and then finding the power series 1r mam) n=0 (b) by long division (Give the first three terms.) )0 =S 2. [-l2 Points] I DETAILS I LARCALC129.1.051. I MY NOTES I ASK Find the nth term, an, of the sequence. (Your formula should work for n = 1, 2, ....) 9,8+i,8+l,8+i,8+i,... 2 3 4 5 III II Determine whether the sequence you have chosen converges or diverges. 20. [-/1 Points] DETAILS LARCALC12 9.10.009. Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f (X ) = 5 C =1 X f ( x ) = n = 03. [-/2 Points] DETAILS LARCALC12 9.2.061. Find all values of x for which the series converges. (Enter your answer using interval notation.) ( 6x)" n = 1 For these values of x, write the sum of the series as a function of x. f ( x ) =4. [-/1 Points] DETAILS LARCALC12 9.2.031. Find the sum of the convergent series. 20 n(n + 2) n= 15. [-/2 Points] DETAILS LARCALC12 9.3.005. Confirm that the Integral Test can be applied to the series. n = Evaluate the following. 1 dx = Use the Integral Test to determine the convergence or divergence of the series. O converges O diverges7. [-12 Points] DETAILS LARCALC1Z 9.6.025. MY NOTES ASK YOUR TEACHER PRAC Consider the following series. so n2 n n=19 Using the Ratio Test, find the fol owing limit. (If the limit is infinite, enter 'cc' or '-oo', as appropriate. If the limit does not otherwise exist, enter DNE.) lim n>m 'an+1'= an Determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. converges diverges 8. [-/2 Points] DETAILS LARCALC12 9.6.030. MY NOTES ASK YOUR TEACHER Consider the following series. (2n) ! 8 n = : Using the Ratio Test, find the following limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim an + 1 n - 00 an Determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. converges diverges9. [-/2 Points] DETAILS LARCALC12 9.6.040. MY NOTES Consider the following series. n = Using the Root Test, find the following limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim V la l = n - 00 Determine the convergence or divergence of the series. If the Root Test is inconclusive, determine the convergence or divergence of the series using other methods. converges diverges