1.

The value of `lim_(x to 0) (15^(x) - 5^(x) - 3^(x) + 1)/(1 - cos 2x) ` isA. `((log 3) (log 5))/(2)`B. 2 (log 3) (log 5)C. `(log 3 + log 5)/(2)`D. None of these

Answer» Correct Answer - A
`underset(x to 0) ("lim") (15^(x) - 5^(x) - 3^(x) + 1)/(1 - cos 2x)`
`underset(x to 0)("lim") ((3^(x) - 1) (5^(x) - 1))/(1-1 + 2 sin^(2) x)`
`= underset(x to 0) ("lim") ((3^(x) - 1)/(x)) ((5^(x) - 1)/(x)) ((x^(2))/(2 sin^(2) x))`
`= (1)/(2) (log 3) (log 5) * 1`
`[ because underset(x to 0)("lim") ((a^(x) - b^(x))/(x)) = log ((a)/(b))]`


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