What is taylor f(x)=e^{x^2} ?

The answer to taylor f(x)=e^{x^2} is 1+x^2+1/2 x^4+1/6 x^6+1/24 x^8+\ldots

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taylor f(x)=e^{x^2}

taylor

f (x) = e^{x^{2}}

1 + x^{2} + \frac{1}{2} x^{4} + \frac{1}{6} x^{6} + \frac{1}{24} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{12}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{120}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1680}{8 !} x^{8} + \dots

Refine

= 1 + x^{2} + \frac{1}{2} x^{4} + \frac{1}{6} x^{6} + \frac{1}{24} x^{8} + \dots

n \to \infty lim ((- 1)^{n})

\frac{d}{d x} (\frac{x ^{3}}{3 - 6 x ^{2} + 8 x - 7})

\int 8 x 1 - x^{2} d x

\frac{d}{d x} (\frac{20 x ^{2}}{( x - 1 ) ^{3}})

f (x) = \frac{1}{( 2 x - 1 ) ^{6}}, at x = 1

What is taylor f(x)=e^{x^2} ?
The answer to taylor f(x)=e^{x^2} is 1+x^2+1/2 x^4+1/6 x^6+1/24 x^8+\ldots