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Analytic and Harmonic Functions — Howell & Matthews
Mathematics — Complex Analysis · lhopitals-rule-complex
Problem Use L'H\^opital's rule to find the following limits.
(a) lim z → i z 4 − 1 z − i \displaystyle\lim_{z\to i}\frac{z^4-1}{z-i} z → i lim z − i z 4 − 1 lim z → 1 + i z 2 − i z − 1 − i z 2 − 2 z + 2 \displaystyle\lim_{z\to 1+i}\frac{z^2-iz-1-i}{z^2-2z+2} z → 1 + i lim z 2 − 2 z + 2 z 2 − i z − 1 − i lim z → − i z 6 + 1 z 2 + 1 \displaystyle\lim_{z\to -i}\frac{z^6+1}{z^2+1} z → − i lim z 2 + 1 z 6 + 1 lim z → 1 + i z 4 + 4 z 2 − 2 z + 2 \displaystyle\lim_{z\to 1+i}\frac{z^4+4}{z^2-2z+2} z → 1 + i lim z 2 − 2 z + 2 z 4 + 4 lim z → 1 + i 3 z 6 − 64 z 3 + 8 \displaystyle\lim_{z\to 1+i\sqrt{3}}\frac{z^6-64}{z^3+8} z → 1 + i 3 lim z 3 + 8 z 6 − 64 lim z → − 1 + i 3 z 9 − 512 z 3 − 8 \displaystyle\lim_{z\to -1+i\sqrt{3}}\frac{z^9-512}{z^3-8} z → − 1 + i 3 lim z 3 − 8 z 9 − 512 Browse the problem library