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Question
Evaluate the following limits:
`lim_(x -> pi) (1 + sinx)^(2"cosec"x)`
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Solution
`lim_(x -> pi) (1 + sinx)^(2"cosec"x) = lim_(x -> pi)(1 + sinx)^(2/sinx)`
Put y = sin x
When x = `pi/2` the y = `sin pi/2` = 1
`lim_(x -> pi) (1 + sinx)^(2"cosec"x) = lim_(y ->1)(1 +y)^(2/y)`
= `(1 + 1)^(2/1)`
= 22
= 4
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