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) ez 26) ezez

Critical thinking questions:

27) Evaluate: ii 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 iin ln iin

25) ez 26) ezez ln iin ln iin   

Critical thinking questions:  27) Evaluate: ii 28) Evaluate: ln i i  e

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