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Question
Evaluate the following limit:
`lim_(z -> -5)[((1/z + 1/5))/(z + 5)]`
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Solution
`lim_(z -> -5)[(1/z + 1/5)/(z + 5)]`
= `lim_(z -> -5) (((5 + z)/(5z)))/(z + 5)`
= `lim_(z -> - 5) 1/(5z)` ...[∵ z → – 5, z ≠ – 5 ∴ z + 5 ≠ 0]
= `(lim_(z -> - 5)(1))/(lim_(z -> - 5) (5z))`
= `1/(5( - 5))`
= `-1/25`
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