What is maclaurin ln(2+x) ?

The answer to maclaurin ln(2+x) is ln(2)+1/2 x-1/8 x^2+1/24 x^3-1/64 x^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

maclaurin ln(2+x)

maclaurin

ln (2 + x)

ln (2) + \frac{1}{2} x - \frac{1}{8} x^{2} + \frac{1}{24} x^{3} - \frac{1}{64} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= ln (2) + \frac{\frac{1}{2}}{1 !} x + \frac{- \frac{1}{4}}{2 !} x^{2} + \frac{\frac{1}{4}}{3 !} x^{3} + \frac{- \frac{3}{8}}{4 !} x^{4} + \dots

Refine

= ln (2) + \frac{1}{2} x - \frac{1}{8} x^{2} + \frac{1}{24} x^{3} - \frac{1}{64} x^{4} + \dots

\frac{d}{d x} (5 arctan (x + 1 + x^{2}))

\frac{d y}{d x} = 0.0015 y (1200 - y)

\int \frac{1}{7 - 8 x} d x

f (x) = 5 x

\frac{d w}{d t}

What is maclaurin ln(2+x) ?
The answer to maclaurin ln(2+x) is ln(2)+1/2 x-1/8 x^2+1/24 x^3-1/64 x^4+\ldots