What is taylor 3/(x+3)-sqrt(5-2x),0 ?

The answer to taylor 3/(x+3)-sqrt(5-2x),0 is

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taylor 3/(x+3)-sqrt(5-2x),0

taylor

\frac{3}{x + 3} - 5 - 2 x, 0

1 - 5 + \frac{- 5 + 3}{3 5} x + \frac{10 5 + 9}{90 5} x^{2} + \frac{- 50 5 + 27}{1350 5} x^{3} + \frac{200 5 + 81}{16200 5} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 - 5 + \frac{\frac{d}{d x} ( \frac{3}{x + 3} - 5 - 2 x ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{3}{x + 3} - 5 - 2 x ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{3}{x + 3} - 5 - 2 x ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 - 5 + \frac{- \frac{1}{3} + \frac{1}{5}}{1 !} x + \frac{\frac{2}{9} + \frac{1}{5 5}}{2 !} x^{2} + \frac{- \frac{2}{9} + \frac{3}{25 5}}{3 !} x^{3} + \frac{\frac{8}{27} + \frac{3}{25 5}}{4 !} x^{4} + \dots

Refine

= 1 - 5 + \frac{- 5 + 3}{3 5} x + \frac{10 5 + 9}{90 5} x^{2} + \frac{- 50 5 + 27}{1350 5} x^{3} + \frac{200 5 + 81}{16200 5} x^{4} + \dots

\int \frac{x ^{- 2} - 4}{x ^{3}} d x

\int sin^{5} (5 x) cos^{2} (5 x) d x

\int \frac{x}{x ^{2} + x + 2} d x

\frac{d}{d x} (\frac{2 x ^{3} + 5}{4 x ^{2} + 7})

\frac{d}{d x} ((f (x) (x^{3}))^{2})

What is taylor 3/(x+3)-sqrt(5-2x),0 ?
The answer to taylor 3/(x+3)-sqrt(5-2x),0 is