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

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

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taylor (e^x)/(cos(x))

taylor

\frac{e ^{x}}{cos ( x )}

1 + x + x^{2} + \frac{2}{3} x^{3} + \frac{1}{2} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{2}{2 !} x^{2} + \frac{4}{3 !} x^{3} + \frac{12}{4 !} x^{4} + \dots

Refine

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

\int sin (3 z) cos^{2} (3 z) d z

\int x sec^{2} (x^{2}) d x

n = 0 \sum \infty (\frac{1}{5})^{n}

12 arcsin (e^{\frac{x}{2}})

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