6.1

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1_ circle around the answer 2- Your handwriting is special so I can understand 3- I just want the answers

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1. [2/3 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 6.1.005.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following power series. 5(- 1 ) k ( x - 7 ) k 9k Let a, = (-1)k - (x - 7)k. Find the following limit. ak + 1 x - 7 lim K -0 ak 9 Find the interval I and radius of convergence R for the given power series. (Enter your answer for interval of convergence using interval notation.) 1 = (-14,16) X P 9 Need Help? Read It Watch It8. [-I1 Points] ZILLDIFFEQMODAPH 6.1.037.EP. ASK YOUR TEACH ER Consider the following differential equation to be solved using a power series as in Example 4 of Section 4.1. Y. = XV Using the substitution y = Z en?!" nd an expression for the following coefcients. (Give your answers in terms of CO') H = o a=co C; =( )0 c4 = ( )co cs=( >0 :6 = ( )9, Find the solution. (Give your answer in terms of co.) y(x) = 'i( ) n=u Need Help? 9. [-/1 Points] DETAILS ZILLDIFFEQMODAP11 6.1.038. MY NOTES ASK YOUR TEACHER Proceed as in Example 4 in Section 6.1 and find a power series solution y = `c x" of the given linear first-order differential equation. (Give your answer in terms of co.) n =0 (1 + x)y'ty = 0 y ( x ) = co > n = 0 Need Help? Read It10. [0/1 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 7.3.034. MY NOTES ASK YOUR TEACHER PR Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an LRC-series circuit is d'a + Rda + 1q = E(t). dt 2 dt See this excerpt about LRC-series circuits. Use the Laplace transform to find q(t) when _ = 1 h, R = 20 0, C = 0.005 f, E(t) = 170 V, t > 0, q(0) = 0, and i(0) = 0. q(t) = X What is the current i(t)? i(t) = X Need Help? Read It Watch It21. [0.67/1 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 7.3.065. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the Laplace transform to solve the given initial-value problem. y' + 3y = f(t), y(0) = 0, where f(t) = &, Ost