What is taylor e^x+cos(x) ?

The answer to taylor e^x+cos(x) is 2+x+1/6 x^3+1/12 x^4+1/120 x^5+\ldots

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taylor e^x+cos(x)

taylor

e^{x} + cos (x)

2 + x + \frac{1}{6} x^{3} + \frac{1}{12} x^{4} + \frac{1}{120} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 2 + x + \frac{1}{6} x^{3} + \frac{1}{12} x^{4} + \frac{1}{120} x^{5} + \dots

\frac{d}{d x} (sin (x) + sin (y))

x \to - 3 lim (π - x)

\int_{0}^{\infty} t \cdot e^{- t} d t

f (x) = cos (sin^{2} (x))

\int π^{2} r^{4} d r

What is taylor e^x+cos(x) ?
The answer to taylor e^x+cos(x) is 2+x+1/6 x^3+1/12 x^4+1/120 x^5+\ldots