Let a, b, and c denote complex constants. Then use definition (2), Sec. 15, of limits...

 

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Let a, b, and c denote complex constants. Then use definition (2), Sec. 15, of limits to show that: (a) lim z -> z_0 (az+b) = az_0+ b; (limit as z approaches z not) (b) lim z -> z_0 (z^2+ c) = (z_0)^2 + c; (limit as z approaches z not) (c) lim z -> (1-i) [x+i(2x+y)] = 1+i; (limit as z approaches 1 minus i) Definition 2 from sections 15 basically states Epsilon delta informations. These are pretty trivial limits that I understand why they end up being what they are however showing why using that definition is what has me stumped. Let a, b, and c denote complex constants. Then use definition (2), Sec. 15, of limits to show that: (a) lim z -> z_0 (az+b) = az_0+ b; (limit as z approaches z not) (b) lim z -> z_0 (z^2+ c) = (z_0)^2 + c; (limit as z approaches z not) (c) lim z -> (1-i) [x+i(2x+y)] = 1+i; (limit as z approaches 1 minus i) Definition 2 from sections 15 basically states Epsilon delta informations. These are pretty trivial limits that I understand why they end up being what they are however showing why using that definition is what has me stumped.

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