What is maclaurin ln(4+x) ?

The answer to maclaurin ln(4+x) is 2ln(2)+1/4 x-1/32 x^2+1/192 x^3-1/1024 x^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

maclaurin ln(4+x)

maclaurin

ln (4 + x)

2 ln (2) + \frac{1}{4} x - \frac{1}{32} x^{2} + \frac{1}{192} x^{3} - \frac{1}{1024} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 2 ln (2) + \frac{\frac{1}{4}}{1 !} x + \frac{- \frac{1}{16}}{2 !} x^{2} + \frac{\frac{1}{32}}{3 !} x^{3} + \frac{- \frac{3}{128}}{4 !} x^{4} + \dots

Refine

= 2 ln (2) + \frac{1}{4} x - \frac{1}{32} x^{2} + \frac{1}{192} x^{3} - \frac{1}{1024} x^{4} + \dots

What is maclaurin ln(4+x) ?
The answer to maclaurin ln(4+x) is 2ln(2)+1/4 x-1/32 x^2+1/192 x^3-1/1024 x^4+\ldots