What is taylor sqrt((1+x)/(1-x)) ?

The answer to taylor sqrt((1+x)/(1-x)) is 1+x+1/2 x^2+1/2 x^3+3/8 x^4+\ldots

Popular >

taylor sqrt((1+x)/(1-x))

taylor

\frac{1 + x}{1 - x}

1 + x + \frac{1}{2} x^{2} + \frac{1}{2} x^{3} + \frac{3}{8} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{1}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{9}{4 !} x^{4} + \dots

Refine

= 1 + x + \frac{1}{2} x^{2} + \frac{1}{2} x^{3} + \frac{3}{8} x^{4} + \dots

\frac{d y}{d x} + 5 y = 9

\int arccot (14 y) d y

(2 x + 1) y^{^{'}} = 4 x + 2 y

\int \frac{sin ^{3} ( 5 x )}{cos ^{4} ( 5 x )} d x

x \to 0 - lim (\frac{1}{x ^{\frac{2}{3}}})

What is taylor sqrt((1+x)/(1-x)) ?
The answer to taylor sqrt((1+x)/(1-x)) is 1+x+1/2 x^2+1/2 x^3+3/8 x^4+\ldots