en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor 1/(2x),\at 2

Solution

taylor

\frac{1}{2 x}, at 2

Solution

\frac{- \frac{1}{2 ( at 2 ) ^{2}}}{1 !} (x - at 2) + \frac{\frac{1}{( at 2 ) ^{3}}}{2 !} (x - at 2)^{2} + \frac{- \frac{3}{( at 2 ) ^{4}}}{3 !} (x - at 2)^{3} + \frac{\frac{12}{( at 2 ) ^{5}}}{4 !} (x - at 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{2 at 2} + \frac{- \frac{1}{2 ( at 2 ) ^{2}}}{1 !} (x - at 2) + \frac{\frac{1}{( at 2 ) ^{3}}}{2 !} (x - at 2)^{2} + \frac{- \frac{3}{( at 2 ) ^{4}}}{3 !} (x - at 2)^{3} + \frac{\frac{12}{( at 2 ) ^{5}}}{4 !} (x - at 2)^{4} + \dots

Refine

= \frac{- \frac{1}{2 ( at 2 ) ^{2}}}{1 !} (x - at 2) + \frac{\frac{1}{( at 2 ) ^{3}}}{2 !} (x - at 2)^{2} + \frac{- \frac{3}{( at 2 ) ^{4}}}{3 !} (x - at 2)^{3} + \frac{\frac{12}{( at 2 ) ^{5}}}{4 !} (x - at 2)^{4} + \dots

Popular Examples

limit as x approaches 0 of ((sin(2x)))/x

x \to 0 lim (\frac{( sin ( 2 x ) )}{x})

(dy)/(dx)=-yx^2

\frac{d y}{d x} = - y x^{2}

derivative of-(x^2+3x-2^3)

\frac{d}{d x} (- (x^{2} + 3 x - 2)^{3})

parity y=xsin(x)+cot(x)parity

y = x sin (x) + cot (x)

derivative of ((x+1^2)/((x-1)^2))

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

Frequently Asked Questions (FAQ)

What is taylor 1/(2x),\at 2 ?
The answer to taylor 1/(2x),\at 2 is