What is taylor e^{2x-3},1 ?

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

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taylor e^{2x-3},1

taylor

e^{2 x - 3}, 1

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

x \to 2 lim (5 x^{3} - 6 x - 1)

\int (x^{- \frac{2}{7}}) d x

\frac{d y}{d x}, y = x^{5} + 8

x \to - 1 lim (2 x + 3)

\int_{- π}^{π} cos (2 x) cos (n x) d x

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