What is taylor sqrt(1-x),0 ?

The answer to taylor sqrt(1-x),0 is 1-1/2 x-1/8 x^2-1/16 x^3-5/128 x^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor sqrt(1-x),0

taylor

1 - x, 0

1 - \frac{1}{2} x - \frac{1}{8} x^{2} - \frac{1}{16} x^{3} - \frac{5}{128} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{1}{2}}{1 !} x + \frac{- \frac{1}{4}}{2 !} x^{2} + \frac{- \frac{3}{8}}{3 !} x^{3} + \frac{- \frac{15}{16}}{4 !} x^{4} + \dots

Refine

= 1 - \frac{1}{2} x - \frac{1}{8} x^{2} - \frac{1}{16} x^{3} - \frac{5}{128} x^{4} + \dots

y^{^{'''}} + 3 y^{^{''}} - 4 y = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = cos (2 x)

y^{^{'}} + y - e^{x} = 0

y = x, y = x^{3}, [- 1, 2]

\int - e^{2 t} d t

What is taylor sqrt(1-x),0 ?
The answer to taylor sqrt(1-x),0 is 1-1/2 x-1/8 x^2-1/16 x^3-5/128 x^4+\ldots