What is taylor e^{2z} ?

The answer to taylor e^{2z} is 1+2z+2z^2+4/3 z^3+2/3 z^4+\ldots

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taylor e^{2z}

taylor

e^{2 z}

1 + 2 z + 2 z^{2} + \frac{4}{3} z^{3} + \frac{2}{3} z^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{2}{1 !} z + \frac{4}{2 !} z^{2} + \frac{8}{3 !} z^{3} + \frac{16}{4 !} z^{4} + \dots

Refine

= 1 + 2 z + 2 z^{2} + \frac{4}{3} z^{3} + \frac{2}{3} z^{4} + \dots

4 sin^{2} (x)

\int 28 arctan (x) d x

\frac{d}{d x} (2 y e^{- x})

\frac{d y}{d x} = \frac{( 1 - x - y )}{x + y}

\frac{d}{d x} (x^{2} - 4 x y + 4 y^{2} + 2)

What is taylor e^{2z} ?
The answer to taylor e^{2z} is 1+2z+2z^2+4/3 z^3+2/3 z^4+\ldots