What is taylor 4/x ,3 ?

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

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taylor 4/x ,3

taylor

\frac{4}{x}, 3

\frac{4}{3} - \frac{4}{9} (x - 3) + \frac{4}{27} (x - 3)^{2} - \frac{4}{81} (x - 3)^{3} + \frac{4}{243} (x - 3)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{4}{3} + \frac{- \frac{4}{9}}{1 !} (x - 3) + \frac{\frac{8}{27}}{2 !} (x - 3)^{2} + \frac{- \frac{8}{27}}{3 !} (x - 3)^{3} + \frac{\frac{32}{81}}{4 !} (x - 3)^{4} + \dots

Refine

= \frac{4}{3} - \frac{4}{9} (x - 3) + \frac{4}{27} (x - 3)^{2} - \frac{4}{81} (x - 3)^{3} + \frac{4}{243} (x - 3)^{4} + \dots

t \to 1 lim (\frac{t ^{2} - 1}{t - 1})

\int_{1}^{b} \frac{1}{( x + 6 ) ^{2}} d x

f (x) = ln (4 - x^{2})

\int t^{2} sin (βt) d t

\int x (x^{2} + 3)^{100} d x

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