Complex Analysis: Theory and Applications · Problem 5.4.9

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-trig-limits

Problem

Show that (a) lim⁡z→0cos⁡z−1z=0\displaystyle\lim_{z \to 0} \frac{\cos z - 1}{z} = 0. (b) lim⁡y→+∞tan⁡(x0+iy)=i\displaystyle\lim_{y \to +\infty} \tan(x_0 + iy) = i, where x0x_0 is any fixed real number.

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