What is taylor e^{(x-1)^2} ?

The answer to taylor e^{(x-1)^2} is e-2ex+3ex^2-(10e)/3 x^3+(19e)/6 x^4+\ldots

Popular >

taylor e^{(x-1)^2}

taylor

e^{(x - 1)^{2}}

e - 2 e x + 3 e x^{2} - \frac{10 e}{3} x^{3} + \frac{19 e}{6} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= e + \frac{- 2 e}{1 !} x + \frac{6 e}{2 !} x^{2} + \frac{- 20 e}{3 !} x^{3} + \frac{76 e}{4 !} x^{4} + \dots

Refine

= e - 2 e x + 3 e x^{2} - \frac{10 e}{3} x^{3} + \frac{19 e}{6} x^{4} + \dots

\int_{0}^{\infty} t^{2} d t

\int \frac{x ^{- \frac{1}{2}}}{1 + x ^{\frac{1}{2}}} d x

\frac{1}{4 x - 3}

\int_{0}^{1} 5 e^{- 3 x} d x

\int_{7}^{9} (x^{2} + 2 x - 4) d x

What is taylor e^{(x-1)^2} ?
The answer to taylor e^{(x-1)^2} is e-2ex+3ex^2-(10e)/3 x^3+(19e)/6 x^4+\ldots