What is taylor e^{2x-3} ?

The answer to taylor e^{2x-3} is 1/(e^3)+2/(e^3)x+2/(e^3)x^2+4/(3e^3)x^3+2/(3e^3)x^4+\ldots

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taylor e^{2x-3}

taylor

e^{2 x - 3}

\frac{1}{e ^{3}} + \frac{2}{e ^{3}} x + \frac{2}{e ^{3}} x^{2} + \frac{4}{3 e ^{3}} x^{3} + \frac{2}{3 e ^{3}} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

\frac{\partial}{\partial x} (\frac{1}{3 x ^{2} + y})

x \to - 3 lim (g (x) (f (x)))

\int x (1 - x)^{10} d x

\frac{\partial}{\partial x} (\frac{y}{x ^{2} - y ^{2}})

\frac{d}{d x} (2 x lo g_{10} (x))

What is taylor e^{2x-3} ?
The answer to taylor e^{2x-3} is 1/(e^3)+2/(e^3)x+2/(e^3)x^2+4/(3e^3)x^3+2/(3e^3)x^4+\ldots