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

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

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maclaurin e^{sin(x)}

maclaurin

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 Maclaurin 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

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