What is taylor (x^3-2x+4),2 ?

The answer to taylor (x^3-2x+4),2 is 8+10(x-2)+6(x-2)^2+(x-2)^3

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taylor (x^3-2x+4),2

taylor

(x^{3} - 2 x + 4), 2

8 + 10 (x - 2) + 6 (x - 2)^{2} + (x - 2)^{3}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 8 + \frac{10}{1 !} (x - 2) + \frac{12}{2 !} (x - 2)^{2} + \frac{6}{3 !} (x - 2)^{3} + \frac{0}{4 !} (x - 2)^{4} + \frac{0}{5 !} (x - 2)^{5} + \frac{0}{6 !} (x - 2)^{6} + \frac{0}{7 !} (x - 2)^{7} + \frac{0}{8 !} (x - 2)^{8} + \frac{0}{9 !} (x - 2)^{9} + \frac{0}{10 !} (x - 2)^{10}

Refine

= 8 + 10 (x - 2) + 6 (x - 2)^{2} + (x - 2)^{3}

\int (\frac{1}{2 x ^{2} - 5 x + 7} + (2 x + 3) e^{2 x}) d x

\frac{d}{d x} (x (x - 4)^{2})

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 6)

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

cos (\frac{x}{2})

What is taylor (x^3-2x+4),2 ?
The answer to taylor (x^3-2x+4),2 is 8+10(x-2)+6(x-2)^2+(x-2)^3