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

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

Popular >

taylor e^{(x^2)}

taylor

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

x \to 1 + lim (\frac{2 x + 1}{x - 1})

y^{^{''}} + 12 y^{^{'}} + 37 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int_{0}^{1} \frac{23}{4 y - 1} d y

f (x) = cos^{3} (π x)

\int \frac{x ^{2} - 400}{x} d x

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