What is taylor x^2e^{2x} ?

The answer to taylor x^2e^{2x} is x^2+2x^3+2x^4+4/3 x^5+2/3 x^6+\ldots

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taylor x^2e^{2x}

taylor

x^{2} e^{2 x}

x^{2} + 2 x^{3} + 2 x^{4} + \frac{4}{3} x^{5} + \frac{2}{3} x^{6} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{12}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \frac{160}{5 !} x^{5} + \frac{480}{6 !} x^{6} + \dots

Refine

= x^{2} + 2 x^{3} + 2 x^{4} + \frac{4}{3} x^{5} + \frac{2}{3} x^{6} + \dots

What is taylor x^2e^{2x} ?
The answer to taylor x^2e^{2x} is x^2+2x^3+2x^4+4/3 x^5+2/3 x^6+\ldots