What is taylor 1/(sqrt(4-x)) ?

The answer to taylor 1/(sqrt(4-x)) is 1/2+1/16 x+3/256 x^2+5/2048 x^3+35/65536 x^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

taylor 1/(sqrt(4-x))

taylor

\frac{1}{4 - x}

\frac{1}{2} + \frac{1}{16} x + \frac{3}{256} x^{2} + \frac{5}{2048} x^{3} + \frac{35}{65536} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( \frac{1}{4 - x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{4 - x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{4 - x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{2} + \frac{\frac{1}{16}}{1 !} x + \frac{\frac{3}{128}}{2 !} x^{2} + \frac{\frac{15}{1024}}{3 !} x^{3} + \frac{\frac{105}{8192}}{4 !} x^{4} + \dots

Refine

= \frac{1}{2} + \frac{1}{16} x + \frac{3}{256} x^{2} + \frac{5}{2048} x^{3} + \frac{35}{65536} x^{4} + \dots

\int θ cos^{2} (θ) d θ

d er i v a t i v e y = (\frac{x}{7} + 9)^{\frac{3}{2}}

\frac{d}{d x} (\frac{x - 1}{x ^{2} + x - 2})

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

d er i v a t i v e f (x) = 2 ln (x)

What is taylor 1/(sqrt(4-x)) ?
The answer to taylor 1/(sqrt(4-x)) is 1/2+1/16 x+3/256 x^2+5/2048 x^3+35/65536 x^4+\ldots