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Question
Evaluate the following Limits: `lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`
Solution
`lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`
= `lim_(x -> 0) log[100 (0.01 + x)]/x`
= `lim_(x -> 0) (log(1 + 100x))/x`
= `lim_(x -> 0)[(log(1 + 100x))/(100x)] xx 100`
= 1 x 100 ...`[("As" x -> 0"," 100 x -> 0 and ),(lim_(x -> 0) (log(1 + x))/x = 1)]`
= 100
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