What is taylor e^x,5 ?

The answer to taylor e^x,5 is e^5+e^5(x-5)+(e^5)/2 (x-5)^2+(e^5)/6 (x-5)^3+(e^5)/(24)(x-5)^4+\ldots

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taylor e^x,5

taylor

e^{x}, 5

e^{5} + e^{5} (x - 5) + \frac{e ^{5}}{2} (x - 5)^{2} + \frac{e ^{5}}{6} (x - 5)^{3} + \frac{e ^{5}}{24} (x - 5)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= e^{5} + \frac{e ^{5}}{1 !} (x - 5) + \frac{e ^{5}}{2 !} (x - 5)^{2} + \frac{e ^{5}}{3 !} (x - 5)^{3} + \frac{e ^{5}}{4 !} (x - 5)^{4} + \dots

Refine

= e^{5} + e^{5} (x - 5) + \frac{e ^{5}}{2} (x - 5)^{2} + \frac{e ^{5}}{6} (x - 5)^{3} + \frac{e ^{5}}{24} (x - 5)^{4} + \dots

f (x) = \frac{5}{x}, at x = - \frac{1}{5}

\int_{\frac{π}{6}}^{\infty} \frac{2}{x} d x

\int_{5}^{9} \frac{1}{16 + ( x - 5 ) ^{2}} d x

\int_{1}^{4} (\frac{x}{2}) + 1 d x

\frac{d}{d x} ((8 x - 1)^{3} (2 x + 1)^{4})

What is taylor e^x,5 ?
The answer to taylor e^x,5 is e^5+e^5(x-5)+(e^5)/2 (x-5)^2+(e^5)/6 (x-5)^3+(e^5)/(24)(x-5)^4+\ldots