What is taylor 2e^z ?

The answer to taylor 2e^z is 2+2z+z^2+1/3 z^3+1/12 z^4+\ldots

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taylor 2e^z

taylor

2 e^{z}

2 + 2 z + z^{2} + \frac{1}{3} z^{3} + \frac{1}{12} z^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 2 + 2 z + z^{2} + \frac{1}{3} z^{3} + \frac{1}{12} z^{4} + \dots

\frac{d}{d x} (\frac{3 x - 7}{2 x + 4})

f (x) = \frac{7 + tan ( x )}{5 - tan ( x )}

\frac{\partial}{\partial x} (- 3 y cos (3 x))

(x y^{2} - 3 y) d x + (x^{2} y - 3 x) d y = 0

\int \frac{1 - x}{3 e ^{x}} d x

What is taylor 2e^z ?
The answer to taylor 2e^z is 2+2z+z^2+1/3 z^3+1/12 z^4+\ldots