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Question
Evaluate the following limit:
`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 - 2)(z - 3))/((z - 2)(z + 2))`
= `lim_(z -> 2) (z - 3)/(z + 2) ...[(because z -> 2"," z ≠ 2),(therefore z - 2 ≠ 0)]`
= `(lim_(z -> z) (z - 3))/(lim_(z -> 2)(z + 2))`
= `(2 - 3)/(2 + 2)`
= `-1/4`
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