What is taylor 5xe^x ?

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

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taylor 5xe^x

taylor

5 x e^{x}

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

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 5 x e ^{x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 5 x e ^{x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 5 x e ^{x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{5}{1 !} x + \frac{10}{2 !} x^{2} + \frac{15}{3 !} x^{3} + \frac{20}{4 !} x^{4} + \frac{25}{5 !} x^{5} + \dots

Refine

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

x \to 0 lim (\frac{3 - 2 x}{x ^{4}})

\int \frac{3 x ^{2} - 5 x - 17}{( x + 3 ) ( x - 2 ) ^{2}} d x

\frac{\partial}{\partial x} (2 x^{3} y - 1)

\int (e^{x} + x^{2} - 2^{x}) d x

\frac{1}{8} \frac{d ^{2} x}{d t ^{2}} = - 2 x - 1 \frac{d x}{d t}

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