What is taylor e^x,3 ?

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

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taylor e^x,3

taylor

e^{x}, 3

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

y = 5 x, at x = 4, x = 9

\int_{1}^{3} x e^{- x} d x

\int sec^{2} (2 t) d t

\frac{\partial}{\partial z} (x + yz)

t \to \infty lim (e^{2 t})

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