What is maclaurin ln(3+x) ?

The answer to maclaurin ln(3+x) is ln(3)+1/3 x-1/18 x^2+1/81 x^3-1/324 x^4+\ldots

maclaurin ln(3+x)

maclaurin

ln (3 + x)

ln (3) + \frac{1}{3} x - \frac{1}{18} x^{2} + \frac{1}{81} x^{3} - \frac{1}{324} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= ln (3) + \frac{\frac{1}{3}}{1 !} x + \frac{- \frac{1}{9}}{2 !} x^{2} + \frac{\frac{2}{27}}{3 !} x^{3} + \frac{- \frac{2}{27}}{4 !} x^{4} + \dots

Refine

= ln (3) + \frac{1}{3} x - \frac{1}{18} x^{2} + \frac{1}{81} x^{3} - \frac{1}{324} x^{4} + \dots

\int \frac{1}{x ^{2} x ^{2} - 25} d x

d er i v a t i v e f (x) = 3 sin (x) + 3 cos (x)

s l o p e (- 4, 8), (- 3, 8)

d er i v a t i v e sin (\frac{1}{x ^{2}})

f^{^{''}} (x) = 9 x^{3} + 4 x^{2} + 7 x

What is maclaurin ln(3+x) ?
The answer to maclaurin ln(3+x) is ln(3)+1/3 x-1/18 x^2+1/81 x^3-1/324 x^4+\ldots