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Show epsilon arguments for any limit proofs: 1)Prove: If limf(x)x->a=L and c∈R, then limx->acf(x)=cL. 2) Prove:...

Show epsilon arguments for any limit proofs:


1)Prove: If limf(x)x->a=L and c∈R, then limx->acf(x)=cL.
2) Prove: If lim f(x)x->a = L and lim g(x)x->a = M, then lim(f(x)+g(x))​​​​​​​x->a = L+M.

3) Find a counterexample to the converse of #2.

4) Prove: If lim f(x)​​​​​​​x->a = L and lim g(x)​​​​​​​x->a = M, then lim(f(x)g(x)) ​​​​​​​x->a= LM.

5) Find a counterexample to the converse of #4.

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