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

Answer 1

Isabella Ackerman

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

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#

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Answer 2

Christopher Allers

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

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.