Question

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

Answer 1

`lim_{x -> oo} frac{e^{2x}}{x^2} = oo`

Explanation:

Since both the numerator and denominator approaches infinity, we can use L'Hospital Rule.

`lim_{x -> oo} frac{e^{2x}}{x^2} = lim_{x -> oo} frac{frac{"d"}{"d"x}(e^{2x})}{frac{"d"}{"d"x}(x^2)}`

`= lim_{x -> oo} frac{2e^{2x}}{2x}`

`= lim_{x -> oo} frac{e^{2x}}{x}`

The above expression is again indeterminate and we have to use L'Hospital Rule again

`lim_{x -> oo} frac{e^{2x}}{x} = lim_{x -> oo} frac{frac{"d"}{"d"x}(e^{2x})}{frac{"d"}{"d"x}(x)}`

`= lim_{x -> oo} frac{2e^{2x}}{1}`

`= +oo`