What is taylor sqrt(1+2x) ?

The answer to taylor sqrt(1+2x) is 1+x-1/2 x^2+1/2 x^3-5/8 x^4+\ldots

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taylor sqrt(1+2x)

taylor

1 + 2 x

1 + x - \frac{1}{2} x^{2} + \frac{1}{2} x^{3} - \frac{5}{8} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{- 1}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{- 15}{4 !} x^{4} + \dots

Refine

= 1 + x - \frac{1}{2} x^{2} + \frac{1}{2} x^{3} - \frac{5}{8} x^{4} + \dots

x \to 2 lim (\frac{3 x + 4}{8 x - 1})

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

\int x x^{'} d x

\frac{400}{s ( s ^{2} + 200 )}

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

What is taylor sqrt(1+2x) ?
The answer to taylor sqrt(1+2x) is 1+x-1/2 x^2+1/2 x^3-5/8 x^4+\ldots