What is taylor e^{2x+2} ?

The answer to taylor e^{2x+2} is e^2+2e^2x+2e^2x^2+(4e^2)/3 x^3+(2e^2)/3 x^4+\ldots

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taylor e^{2x+2}

taylor

e^{2 x + 2}

e^{2} + 2 e^{2} x + 2 e^{2} x^{2} + \frac{4 e ^{2}}{3} x^{3} + \frac{2 e ^{2}}{3} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= e^{2} + 2 e^{2} x + 2 e^{2} x^{2} + \frac{4 e ^{2}}{3} x^{3} + \frac{2 e ^{2}}{3} x^{4} + \dots

x \to \infty lim (0. 7^{x})

\frac{d y}{d x} + tan (x) y - cos (x) = 0

\int 6 x^{2} - 8 x d x

\int 8 - x d x

\frac{d x}{d t} + \frac{x}{25} = 0.16

What is taylor e^{2x+2} ?
The answer to taylor e^{2x+2} is e^2+2e^2x+2e^2x^2+(4e^2)/3 x^3+(2e^2)/3 x^4+\ldots