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Question
Evaluate the following:
`lim_(x ->0)[((25)^x - 2(5)^x + 1)/x^2]`
Solution
`lim_(x ->0)[((25)^x - 2(5)^x + 1)/x^2]`
= `lim_(x -> 0)[((5)^(2x) - 2(5)^x + 1)/x^2]`
= `lim_(x -> 0)[((5^x)^(2) - 2(5)^x + 1)/x^2]`
= `lim_(x -> 0) [(5^x - 1)^2/x^2]`
= `lim_(x -> 0) ((5^x - 1)/x)^2`
= `log5^2 ...[lim_(x -> 0) ("a"^x - 1)/x = log"a"]`
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