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Question
Evaluate the following limits:
`lim_(x -> 2) (1/x - 1/2)/(x - 2)`
Solution
`lim_(x -> 2) (1/x - 1/2)/(x - 2) = lim_(x -> 2) (((2 - x)/(2x))/(x - 2))`
= `lim_(x -> 2) (-(x - 2))/(2x( x - 2))`
= `- lim_(x -> 2) 1/(2x)`
= `- 1/(2 xx 2)`
`lim_(x -> 2) (1/x - 1/2)/(x - 2) = - 1/4`
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