Please provide solutions so I can properly teach my child. Thank you

1. Evaluate the following limits. Show all work to justify your solutions. Let c be constant. 3 (a) lim Vcth - Vc 3 (b) lim 202 - 2 cx + c2 ath h -+ 0 h 202 - C2 (c) lim h-+0 h 2. Determine for what value(s) of k the limit exists, then solve. lim 203 + 13 2 4 -3 x+3 3. Determine if the statement is true or false. If false, provide a counterexample. (a) Given any real value k, if both lim f(x) and lim g(x) exist, then lim [f(x) +g(x)] must I -+ K also exist. (b) Given any real value k, if lim [f(x) +g(x)] exists, then both lim f(x) and lim g(x) must also exist. I -+ K (c) Given any real value k, if both lim f(x) and lim g(x) exist, then lim f(I) I -+ K r-k g(x) must also exist. (d) Given any real value k, if lim (f o g)(x) exists then both lim f(x) and lim g(x) must also exist