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Question
Evaluate the following limits:
`lim_(x -> oo) (1 + 3/x)^(x + 2)`
Solution
We know `lim_(x -> oo) (1 + "k"/x)^x` = ek
`lim_(x -> oo) (1 + 3/x)^(x + 2) = lim_(x -> oo) (1 + 3/x)^x * (1 + 3/x)^2`
= `lim_(x -> oo) (1 + 3/x)^x xx lim_(x -> oo) (1 + 3/x)^2`
= `"e"^3 xx (1 + 3/oo)^2`
= `"e"^3 xx (1 + 0)`
= e3
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