What is taylor e^{5x} ?

The answer to taylor e^{5x} is 1+5x+25/2 x^2+125/6 x^3+625/24 x^4+\ldots

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taylor e^{5x}

taylor

e^{5 x}

1 + 5 x + \frac{25}{2} x^{2} + \frac{125}{6} x^{3} + \frac{625}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{5 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{5 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{5 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{5}{1 !} x + \frac{25}{2 !} x^{2} + \frac{125}{3 !} x^{3} + \frac{625}{4 !} x^{4} + \dots

Refine

= 1 + 5 x + \frac{25}{2} x^{2} + \frac{125}{6} x^{3} + \frac{625}{24} x^{4} + \dots

\int e^{- 1 + x} d x

\frac{\partial}{\partial r} (e^{r} sin (s t))

\frac{1}{( 1 - 3 x ^{2} )}, x = 0.577

x \to 10 lim (+ (2 x))

(2 x^{3} + 2) (x^{4} - 3 x)

What is taylor e^{5x} ?
The answer to taylor e^{5x} is 1+5x+25/2 x^2+125/6 x^3+625/24 x^4+\ldots