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Question
Select the correct answer from the given alternatives.
`lim_(x -> 0) [(x*log(1 + 3x))/("e"^(3x) - 1)^2]` =
Options
`1/"e"^9`
`1/"e"^3`
`1/9`
`1/3`
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Solution
`1/3`
Explanation;
`lim_(x -> 0) (x*log(1 + 3x))/("e"^(3x) - 1)^2`
= `(lim_(x -> 0) (log(1 + 3x))/x)/(lim_(x -> 0)((e^(3x) - 1)/x)^2`
= `(lim_(x -> 0) [(log(1 + 3x))/(3x) xx 3])/(lim_(x -> 0)[(("e"^(3x) - 1)/(3x))^2 xx (3)^2]`
= `1/3`
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