Answer
See explanations.
Work Step by Step
Step 1. Assume $\lim_{x\to c}f(x)=L_1$ and at the same time, $\lim_{x\to c}f(x)=L_2$
Step 2. Taking the difference of the above two limits, we have $L_1-L_2=\lim_{x\to c}f(x)- \lim_{x\to c}f(x)= \lim_{x\to c}(f(x)-f(x))=0$
Thus $L_1=L_2$
