What is the limit as x approaches 0+of (e^x)/(x^2) ?

The limit as x approaches 0+of (e^x)/(x^2) is infinity

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limit as x approaches 0+of (e^x)/(x^2)

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

\infty

Solution steps

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

\frac{e ^{x}}{x ^{2}} = e^{x} \frac{1}{x ^{2}}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

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

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 2 lim ((x + 1) (x - 3))

x \to 1 lim (x^{2} ln (x))

x \to 2 + lim (3 x)

x \to - 3 lim (9 - 3 x + x^{2})

x \to \frac{π}{2} lim (\frac{5 ( sin ( x ) - 1 )}{cos ^{2} ( x )})

What is the limit as x approaches 0+of (e^x)/(x^2) ?
The limit as x approaches 0+of (e^x)/(x^2) is infinity