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Question
Evaluate the following limits, if necessary use l’Hôpital Rule:
`lim_(x -> oo) "e"^-x sqrt(x)`
Solution
`lim_(x -> oo) "e"^-x sqrt(x)` ......`[0 xx oo "Indeterminate form"]`
The other form is `lim_(x -> oo) sqrt(x)/"e"^x` ......`[0 xx oo "Indeterminate form"]`
Applying L’ Hôpital’s Rule
= `lim_(x -> oo) 1/(2sqrt(x"e"^x)`
= 0
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