What is taylor x^2*e^x ?

The answer to taylor x^2*e^x is x^2+x^3+1/2 x^4+1/6 x^5+1/24 x^6+\ldots

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taylor x^2*e^x

taylor

x^{2} \cdot e^{x}

x^{2} + x^{3} + \frac{1}{2} x^{4} + \frac{1}{6} x^{5} + \frac{1}{24} x^{6} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{12}{4 !} x^{4} + \frac{20}{5 !} x^{5} + \frac{30}{6 !} x^{6} + \dots

Refine

= x^{2} + x^{3} + \frac{1}{2} x^{4} + \frac{1}{6} x^{5} + \frac{1}{24} x^{6} + \dots

x \to - 5 lim (\frac{3 x + 8}{x + 5})

4 t

x \to 14 - lim (ln (14 - x))

y = e^{9 x} cos (π x), (0, 1)

ln (2 - x)

What is taylor x^2*e^x ?
The answer to taylor x^2*e^x is x^2+x^3+1/2 x^4+1/6 x^5+1/24 x^6+\ldots