Kuta Software - Infinite Precalculus Name___________________________________ Power Series Date________________ Period____ Use the fifth partial sum of the exponential series to approximate each value. Round your answer to the nearest thousandth. 1) e 2) e Use the fifth partial sum of the power series for sine or cosine to approximate each value. Round your answer to the nearest thousandth. 3) sin 4) sin Use xn to find a power series representation of g(x). Indicate the interval in which n x the series converges. 5) g(x) 6) g(x) x x 7) g(x) 8) g(x) x x Use xn to find a power series representation of g(x). Indicate the interval in which n x the series converges. Then graph g(x) and the sixth partial sum of its power series. 9) g(x) 10) g(x) x x y y x x -1- Worksheet by Kuta Software LLC ©g b2s0H1R6o eKquptkau VSNoBfDtbwBaerlen [L^LfC].t c AAblulp RrOiIgJh\tTsy UrAeUspeprkvTe_dW.c H uMXaqdfen CwNihtxhK FIenif[i_nDipteeC JPNrreYcgaglec[u]lnuOsO. Write each in exponential form. 11) i 12) i 13) i 14) i Write each in rectangular form. i i 15) e 16) e i i 17) e 18) e Write each as a complex number in rectangular form. 19) ln 20) ln 21) ln 22) ln Solve each equation over the complex numbers. 23) ez 24) ez 25) ez 26) ezez Critical thinking questions: 27) Evaluate: ii 28) Evaluate: ln i -2- Worksheet by Kuta Software LLC ©^ j2]0^1p6s bKCuktka] ISIoifftsw_aHrDeX VLCLeCV._ P cAClIlQ OrSiHgMhvtKsX XrWeSsHeGrRvJe]dL.c o QMIaPdYec hwCiutHhZ mI[ndfZiKnaixtweN MPdrOeycuanlfcAuKlnursk. Kuta Software - Infinite Precalculus Name___________________________________ Power Series Date________________ Period____ Use the fifth partial sum of the exponential series to approximate each value. Round your answer to the nearest thousandth. 1) e 2) e Use the fifth partial sum of the power series for sine or cosine to approximate each value. Round your answer to the nearest thousandth. 3) sin 4) sin Use xn to find a power series representation of g(x). Indicate the interval in which n x the series converges. x n x n 5) g(x) 6) g(x) x n ( ) x n ( ) Converges in: (, ) Converges in: , ( ) n n x 7) g(x) (x ) 8) g(x) x n x n ( ) Converges in: (, ) Converges in: (, ) Use xn to find a power series representation of g(x). Indicate the interval in which n x the series converges. Then graph g(x) and the sixth partial sum of its power series. 9) g(x) 10) g(x) x x y y x x x n (x)n n ( ) n Converges in: (, ) Converges in: (, ) -1- Worksheet by Kuta Software LLC ©X Z2s0j1z6Y iKiuatEae ySmoAfztGwTaPrNek ALXLdCB.D u kAilNlN _rfiMg^hwt]sB SrzePsVeRrIv^eAdY.B G YMpaLdYez jwBiStghO cICnWfpiZnyiVt[ev VP`rgefchaBlMcCu\lQupsp. Write each in exponential form. 11) i 12) i i i e e 13) i 14) i i i e e Write each in rectangular form. i i 15) e 16) e i i i i 17) e 18) e i i Write each as a complex number in rectangular form. 19) ln 20) ln i i 21) ln 22) ln i i Solve each equation over the complex numbers. 23) ez 24) ez ln iin ln iin 25) ez 26) ezez ln iin ln iin Critical thinking questions: 27) Evaluate: ii 28) Evaluate: ln i i e Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com -2- Worksheet by Kuta Software LLC ©[ N2f0i1p6h TKLumtHaw JS\okfZtAwfa]rbeD oLZLkCD.v h gAIlali GrBifghhVtXsL _rFeLs_eSrUvJeCd[.y z iMoaadYeo qwlivtLhy nIGnJfZiDn^iOtJeu nPZrHe`cTatlic`uIlXujsK..