What is taylor sqrt(x),9 ?

The answer to taylor sqrt(x),9 is 3+1/6 (x-9)-1/216 (x-9)^2+1/3888 (x-9)^3-5/279936 (x-9)^4+\ldots

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taylor sqrt(x),9

taylor

x, 9

3 + \frac{1}{6} (x - 9) - \frac{1}{216} (x - 9)^{2} + \frac{1}{3888} (x - 9)^{3} - \frac{5}{279936} (x - 9)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 3 + \frac{\frac{1}{6}}{1 !} (x - 9) + \frac{- \frac{1}{108}}{2 !} (x - 9)^{2} + \frac{\frac{1}{648}}{3 !} (x - 9)^{3} + \frac{- \frac{5}{11664}}{4 !} (x - 9)^{4} + \dots

Refine

= 3 + \frac{1}{6} (x - 9) - \frac{1}{216} (x - 9)^{2} + \frac{1}{3888} (x - 9)^{3} - \frac{5}{279936} (x - 9)^{4} + \dots

f (x) = \frac{5}{x - 4}, at x = 3

\int t^{2} - 5 t + 4 d t

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

f (x) = - 5 x^{2} - 3 x, at x = - 3

\frac{d}{d x} (\frac{3 x + 1}{x ^{\frac{2}{3}}})

What is taylor sqrt(x),9 ?
The answer to taylor sqrt(x),9 is 3+1/6 (x-9)-1/216 (x-9)^2+1/3888 (x-9)^3-5/279936 (x-9)^4+\ldots