What is the limit as x approaches 0 of x^2e^{1/x} ?

The limit as x approaches 0 of x^2e^{1/x} is diverges

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limit as x approaches 0 of x^2e^{1/x}

x \to 0 lim (x^{2} e^{\frac{1}{x}})

diverges

Solution steps

x \to 0 lim (x^{2} e^{\frac{1}{x}})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (x^{2} e^{\frac{1}{x}}) = \infty

x \to 0 - lim (x^{2} e^{\frac{1}{x}}) = 0

= diverges

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

(4.5) (12.8)

x \to 0 lim (\frac{1}{x ^{5}})

x \to 3 lim (\frac{x ^{2}}{x + 1})

\int \frac{- x - 1}{( x ^{2} + 4 x + 5 ) ^{2}} d x

What is the limit as x approaches 0 of x^2e^{1/x} ?
The limit as x approaches 0 of x^2e^{1/x} is diverges