Prove that f(x) is continuous at a if and only if lim

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Lesson Parent: 
Function Limits VI: Continuous Functions
Problem: 

Prove that f(x) is continuous at a if and only if \lim_{h\to 0}\,f(a+h)=f(a).

Answer: 

It is true that f(x) is continuous at a if and only if \lim_{h\to 0}\,f(a+h)=f(a).

SAMPLE SOLUTION

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Solution: 

Recall that when we say "A if and only if B" it means that we need to prove both <Sign in to see all the formulas> and <Sign in to see all the formulas>. For this particular problem we have already show that

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and that

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Therefore,

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