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Question
Evaluate the following limits: `lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`
Solution
`lim_(z -> 2) (z^2 - 5z + 6)/(z^2 - 4)`
= `lim_(z -> 2) ((z - 3)(z - 2))/((z + 2)(z - 2)`
= `lim_(z -> 2) (z - 3)/(z - 2) ...[("As" z -> 2"," z ≠ 2),(therefore z - 2 ≠ 0)]`
= `(2 - 3)/(2 + 2)`
= `-1/4`
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