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

The answer to taylor e^{cos(x)} is e-e/2 x^2+e/6 x^4-(31e)/(720)x^6+\ldots

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taylor e^{cos(x)}

taylor

e^{c o s (x)}

e - \frac{e}{2} x^{2} + \frac{e}{6} x^{4} - \frac{31 e}{720} x^{6} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= e + \frac{0}{1 !} x + \frac{- e}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{4 e}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 31 e}{6 !} x^{6} + \dots

Refine

= e - \frac{e}{2} x^{2} + \frac{e}{6} x^{4} - \frac{31 e}{720} x^{6} + \dots

What is taylor e^{cos(x)} ?
The answer to taylor e^{cos(x)} is e-e/2 x^2+e/6 x^4-(31e)/(720)x^6+\ldots