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CSS Pure Mathematics QUESTION #4107
Question 1
The residue of \(\dfrac{5Z-2}{Z(Z-1)}\) at the pole \(Z=0\) is:
  • \(3\)
  • \(2\)✔️
  • \(5\)
  • \(-2\)
Correct Answer Explanation
Residue at simple pole \(Z=0\): \(\lim_{Z\to0}Z\cdot\dfrac{5Z-2}{Z(Z-1)}=\lim_{Z\to0}\dfrac{5Z-2}{Z-1}=\dfrac{0-2}{0-1}=\dfrac{-2}{-1}=2\). So Res\(_{Z=0}=2\).