What is taylor ln(x^2+2) ?

The answer to taylor ln(x^2+2) is ln(2)+1/2 x^2-1/8 x^4+1/24 x^6-1/64 x^8+\ldots

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taylor ln(x^2+2)

taylor

ln (x^{2} + 2)

ln (2) + \frac{1}{2} x^{2} - \frac{1}{8} x^{4} + \frac{1}{24} x^{6} - \frac{1}{64} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= ln (2) + \frac{0}{1 !} x + \frac{1}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 3}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{30}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 630}{8 !} x^{8} + \dots

Refine

= ln (2) + \frac{1}{2} x^{2} - \frac{1}{8} x^{4} + \frac{1}{24} x^{6} - \frac{1}{64} x^{8} + \dots

y^{^{'}} = 1 + 2 x + y^{2} + 2 x y^{2}

\frac{1}{s - 10}

\frac{\partial}{\partial x} (cos (y) sin (x))

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

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

What is taylor ln(x^2+2) ?
The answer to taylor ln(x^2+2) is ln(2)+1/2 x^2-1/8 x^4+1/24 x^6-1/64 x^8+\ldots