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

The answer to taylor e^{(x^2)/2} is 1+1/2 x^2+1/8 x^4+1/48 x^6+1/384 x^8+\ldots

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taylor e^{(x^2)/2}

taylor

e^{\frac{x ^{2}}{2}}

1 + \frac{1}{2} x^{2} + \frac{1}{8} x^{4} + \frac{1}{48} x^{6} + \frac{1}{384} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{1}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{3}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{15}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{105}{8 !} x^{8} + \dots

Refine

= 1 + \frac{1}{2} x^{2} + \frac{1}{8} x^{4} + \frac{1}{48} x^{6} + \frac{1}{384} x^{8} + \dots

x, x

f (x) = \frac{1}{- 2 + ( 3 x + 1 ) ^{2}}

\int (5 x^{2} + 1) 5 x^{3} + 3 x - 2 d x

\frac{d}{d x} (sinh^{2} (x))

\int x^{2} - 4 x + 3 d x

What is taylor e^{(x^2)/2} ?
The answer to taylor e^{(x^2)/2} is 1+1/2 x^2+1/8 x^4+1/48 x^6+1/384 x^8+\ldots