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

The answer to taylor e^{sin(x)} is 1+x+1/2 x^2-1/8 x^4-1/15 x^5+\ldots

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taylor e^{sin(x)}

taylor

e^{s i n (x)}

1 + x + \frac{1}{2} x^{2} - \frac{1}{8} x^{4} - \frac{1}{15} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{1}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 3}{4 !} x^{4} + \frac{- 8}{5 !} x^{5} + \dots

Refine

= 1 + x + \frac{1}{2} x^{2} - \frac{1}{8} x^{4} - \frac{1}{15} x^{5} + \dots

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

\int (x^{1.7} + 9 x^{3.5}) d x

\frac{d}{d x} (4 + x^{2})

y = (1 + 5 x)^{9}, (0, 1)

y^{2} y^{^{'}} + 5 = x^{2}

What is taylor e^{sin(x)} ?
The answer to taylor e^{sin(x)} is 1+x+1/2 x^2-1/8 x^4-1/15 x^5+\ldots