# Calculus Right Sided Limit Proof

I am trying to prove: If $$\lim_{x\to a^+}f(x)=\infty$$ and $$\lim_{x\to a^+}g(x)=\infty$$, then $$\lim_{x\to a^+}(f(x)+g(x))=\infty$$

This is what I have:

Proof:

$$\forall M_1>0$$, $$\exists\delta_1>0:0M_1$$.

$$\forall M_2>0$$, $$\exists\delta_2>0:0M_2$$.

Let $$M>0$$. Choose $$\delta=min\{\delta_1,\delta_2\}.$$

Thus $$\delta\leq \delta_1$$ and $$\delta\leq\delta_2$$.

Assume $$0.

So, $$f(x)>M_1$$ and $$g(x)>M_2$$.

Show $$f(x)+g(x)>M$$.

I get stuck here and I don't know what to do. If anybody could help, that would be greatly appreciated.

Take $$M>0$$. Since $$\frac M2>0$$, there is some $$\delta_1>0$$ such that $$a\frac M2$$. And there is some $$\delta_2>0$$ such that $$a\frac M2$$. So, if $$\delta=\min\{\delta_1,\delta_2\}$$,$$aM.$$