What is taylor x-x^3,-2 ?

The answer to taylor x-x^3,-2 is 6-11(x+2)+6(x+2)^2-(x+2)^3

taylor x-x^3,-2

taylor

x - x^{3}, - 2

6 - 11 (x + 2) + 6 (x + 2)^{2} - (x + 2)^{3}

Solution steps

Apply the Taylor Formula

= 6 + \frac{\frac{d}{d x} ( x - x ^{3} ) ( - 2 )}{1 !} (x + 2) + \frac{\frac{d ^{2}}{d x ^{2}} ( x - x ^{3} ) ( - 2 )}{2 !} (x + 2)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x - x ^{3} ) ( - 2 )}{3 !} (x + 2)^{3} + \dots

Evaluate Derivatives

= 6 + \frac{- 11}{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

= 6 - 11 (x + 2) + 6 (x + 2)^{2} - (x + 2)^{3}

\frac{\partial}{\partial y} (3 x z^{2} e^{y^{2}})

d er i v a t i v e f (x) = \frac{1}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

\frac{d}{d x} (2 lo g_{10} (x) - 3 x)

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

d er i v a t i v e \frac{3 x + 4}{3 x - 4}

What is taylor x-x^3,-2 ?
The answer to taylor x-x^3,-2 is 6-11(x+2)+6(x+2)^2-(x+2)^3