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CSS Pure Mathematics QUESTION #1274
Question 1
The residue of \(\dfrac{5Z-2}{Z(Z-1)}\) at \(Z=0\) is:
  • \(5\)
  • \(-2\)
  • \(2\)✔️
  • \(3\)
Correct Answer Explanation
Using the residue formula for a simple pole: \(\text{Res}_{Z=0}=\lim_{Z\to0}Z\cdot\dfrac{5Z-2}{Z(Z-1)}=\lim_{Z\to0}\dfrac{5Z-2}{Z-1}=\dfrac{-2}{-1}=2\).