What is taylor (e^t)/(1+t) ?

The answer to taylor (e^t)/(1+t) is 1+1/2 t^2-1/3 t^3+3/8 t^4-11/30 t^5+\ldots

Popular >

taylor (e^t)/(1+t)

taylor

\frac{e ^{t}}{1 + t}

1 + \frac{1}{2} t^{2} - \frac{1}{3} t^{3} + \frac{3}{8} t^{4} - \frac{11}{30} t^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} t + \frac{1}{2 !} t^{2} + \frac{- 2}{3 !} t^{3} + \frac{9}{4 !} t^{4} + \frac{- 44}{5 !} t^{5} + \dots

Refine

= 1 + \frac{1}{2} t^{2} - \frac{1}{3} t^{3} + \frac{3}{8} t^{4} - \frac{11}{30} t^{5} + \dots

f (x) = e^{s i n (3 x)}

\frac{\partial}{\partial x} (y x^{2} + y^{2})

x \to \infty lim (3 x^{3} - 1000 x^{2})

\int \frac{sin ( ln ( x ^{6} ) )}{x} d x

\int \frac{1}{x ^{2} - 2 x - 3} d x

What is taylor (e^t)/(1+t) ?
The answer to taylor (e^t)/(1+t) is 1+1/2 t^2-1/3 t^3+3/8 t^4-11/30 t^5+\ldots