What is taylor 8xe^x,0 ?

The answer to taylor 8xe^x,0 is 8x+8x^2+4x^3+4/3 x^4+1/3 x^5+\ldots

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taylor 8xe^x,0

taylor

8 x e^{x}, 0

8 x + 8 x^{2} + 4 x^{3} + \frac{4}{3} x^{4} + \frac{1}{3} x^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 8 x e ^{x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 8 x e ^{x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 8 x e ^{x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{8}{1 !} x + \frac{16}{2 !} x^{2} + \frac{24}{3 !} x^{3} + \frac{32}{4 !} x^{4} + \frac{40}{5 !} x^{5} + \dots

Refine

= 8 x + 8 x^{2} + 4 x^{3} + \frac{4}{3} x^{4} + \frac{1}{3} x^{5} + \dots

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What is taylor 8xe^x,0 ?
The answer to taylor 8xe^x,0 is 8x+8x^2+4x^3+4/3 x^4+1/3 x^5+\ldots