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Question
Evaluate the following limits, if necessary use l’Hôpital Rule:
`lim_(x -> 1^+) (2/(x^2 - 1) - x/(x - 1))`
Solution
`lim_(x -> 1^+) (2/(x^2 - 1) - x/(x - 1))` ......`[oo - oo "Indeterminate form"]`
Simplifying, we get
= `lim_(x -> 1^+) [(2 - x(x + 1))/(x^2 - 1)]`
= `lim_(x -> 1^+) [(2 - x^2 - x)/(x^2 - 1)]` ........`[0/0 "Indeterminate form"]`
Applying L' Hôpital's rule,
= `lim_(x -> 1^+) (-2x - 1)/(2x)`
= ` - 3/2`
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