What is taylor e^{t^2} ?

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

taylor e^{t^2}

taylor

e^{t^{2}}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

\int e^{x} sec^{2} (e^{x}) d x

y^{^{''}} + 25 y = 20 sin (5 x)

e^{x - y} d x + e^{y - x} d y = 0

d er i v a t i v e f (x^{2})

\frac{\partial}{\partial x} (\frac{1}{e ^{x}})

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