What is taylor 1/(3+2x) ?

The answer to taylor 1/(3+2x) is 1/3-2/9 x+4/27 x^2-8/81 x^3+16/243 x^4+\ldots

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taylor 1/(3+2x)

taylor

\frac{1}{3 + 2 x}

\frac{1}{3} - \frac{2}{9} x + \frac{4}{27} x^{2} - \frac{8}{81} x^{3} + \frac{16}{243} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{3} + \frac{- \frac{2}{9}}{1 !} x + \frac{\frac{8}{27}}{2 !} x^{2} + \frac{- \frac{16}{27}}{3 !} x^{3} + \frac{\frac{128}{81}}{4 !} x^{4} + \dots

Refine

= \frac{1}{3} - \frac{2}{9} x + \frac{4}{27} x^{2} - \frac{8}{81} x^{3} + \frac{16}{243} x^{4} + \dots

\int (x^{4} + x^{2})^{8} (4 x^{3} + 2 x) d x

y^{^{''}} + 4 y = sin (2 x) cos (2 x)

\frac{d}{d x} (21 \cdot π \cdot x^{2})

y = ln (3 x^{2} + 7 y^{2})

\int csc (z + \frac{π}{4}) cot (z + \frac{π}{4}) d z

What is taylor 1/(3+2x) ?
The answer to taylor 1/(3+2x) is 1/3-2/9 x+4/27 x^2-8/81 x^3+16/243 x^4+\ldots