What is taylor e^{5x+5} ?

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

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taylor e^{5x+5}

taylor

e^{5 x + 5}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

x \to - \infty lim (x^{2} - x)

y = \frac{3 x ^{5} + 9}{x ^{3}}

\frac{s ^{2} - 1}{( s - 2 ) ^{6}}

\frac{d y}{d x} + 20 y = sin (x)

\frac{d}{d x} (3 arctan (x))

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