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Question
Evaluate the following limit :
`lim_(x ->0)((secx - 1)/x^2)`
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Solution
`lim_(x ->0)(secx - 1)/x^2`
= `lim_(x -> 0) ((secx - 1)(secx + 1))/(x^2(secx + 1))`
= `lim_(x -> 0) (sec^2 x - 1)/(x^2(secx + 1))`
= `lim_(x -> 0) (tan^2x)/(x^2(secx + 1))`
= `lim_(x -> 0) [(tanx/x)^2 xx 1/(secx + 1)]`
= `lim_(x -> 0) (tanx/x)^2 xx lim_(x -> 0) 1/(secx + 1)`
= `(1)^2 xx 1/(1 + 1)`
= `1/2`
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