What is taylor e^{x^2},0 ?

The answer to taylor e^{x^2},0 is 1+x^2+1/2 x^4+1/6 x^6+1/24 x^8+\ldots

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taylor e^{x^2},0

taylor

e^{x^{2}}, 0

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

\int_{- 1}^{0} x^{3} + 1 d x

18 x - 3 x

f (x) = - 1 - 9 x^{2}, at x = 3

r^{2} - x^{2}

x^{2}, 4

What is taylor e^{x^2},0 ?
The answer to taylor e^{x^2},0 is 1+x^2+1/2 x^4+1/6 x^6+1/24 x^8+\ldots