What is taylor e^{-3z+1}+8 ?

The answer to taylor e^{-3z+1}+8 is e+8-3ez+(9e)/2 z^2-(9e)/2 z^3+(27e)/8 z^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

taylor e^{-3z+1}+8

taylor

e^{- 3 z + 1} + 8

e + 8 - 3 ez + \frac{9 e}{2} z^{2} - \frac{9 e}{2} z^{3} + \frac{27 e}{8} z^{4} + \dots

Solution steps

Apply the Taylor Formula

= e + 8 + \frac{\frac{d}{d z} ( e ^{- 3 z + 1} + 8 ) ( 0 )}{1 !} z + \frac{\frac{d ^{2}}{d z ^{2}} ( e ^{- 3 z + 1} + 8 ) ( 0 )}{2 !} z^{2} + \frac{\frac{d ^{3}}{d z ^{3}} ( e ^{- 3 z + 1} + 8 ) ( 0 )}{3 !} z^{3} + \dots

Evaluate Derivatives

= e + 8 + \frac{- 3 e}{1 !} z + \frac{9 e}{2 !} z^{2} + \frac{- 27 e}{3 !} z^{3} + \frac{81 e}{4 !} z^{4} + \dots

Refine

= e + 8 - 3 ez + \frac{9 e}{2} z^{2} - \frac{9 e}{2} z^{3} + \frac{27 e}{8} z^{4} + \dots

What is taylor e^{-3z+1}+8 ?
The answer to taylor e^{-3z+1}+8 is e+8-3ez+(9e)/2 z^2-(9e)/2 z^3+(27e)/8 z^4+\ldots