What is taylor x^{3/2},4 ?

The answer to taylor x^{3/2},4 is 8+3(x-4)+3/16 (x-4)^2-1/128 (x-4)^3+3/4096 (x-4)^4+\ldots

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taylor x^{3/2},4

taylor

x^{\frac{3}{2}}, 4

8 + 3 (x - 4) + \frac{3}{16} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{3}{4096} (x - 4)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 8 + \frac{\frac{d}{d x} ( x ^{\frac{3}{2}} ) ( 4 )}{1 !} (x - 4) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{3}{2}} ) ( 4 )}{2 !} (x - 4)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{3}{2}} ) ( 4 )}{3 !} (x - 4)^{3} + \dots

Evaluate Derivatives

= 8 + \frac{3}{1 !} (x - 4) + \frac{\frac{3}{8}}{2 !} (x - 4)^{2} + \frac{- \frac{3}{64}}{3 !} (x - 4)^{3} + \frac{\frac{9}{512}}{4 !} (x - 4)^{4} + \dots

Refine

= 8 + 3 (x - 4) + \frac{3}{16} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{3}{4096} (x - 4)^{4} + \dots

\frac{\partial}{\partial x} (- 210 (5 x - y)^{5})

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

y = \frac{6 x}{x ^{2} + 1}

\int_{- 2}^{2} 1 d x

tan (x^{8})

What is taylor x^{3/2},4 ?
The answer to taylor x^{3/2},4 is 8+3(x-4)+3/16 (x-4)^2-1/128 (x-4)^3+3/4096 (x-4)^4+\ldots