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Question
Select the correct answer from the given alternatives.
`lim_(x -> 0) ((15^x - 3^x - 5^x + 1)/sin^2x)` =
Options
log 15
log 3 + log 5
log 3 . log 5
3 log 5
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Solution
log 3 . log 5
Explanation;
`lim_(x -> 0) ((15^x - 3^x - 5^x + 1)/sin^2x)`
= `lim_(x -> 0)[((5^x - 1)(3^x - 1))/x^2 xx x^2/sin^2x] ...[(because x -> 0"," x ≠ 0),(therefore x^2 ≠ 0)]`
= log 3 . log 5
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