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 lim_x->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.

Expert Solution

milcah answered 2 years ago

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