Prove that if \[\lim_{x\to a}\,(f(x)-L)=0,\] then \[\lim_{x\to a}\,f(x)=L.\]

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Lesson Parent: 
Function Limits III: The Gory Details
Problem: 

Prove that if \[\lim_{x\to a}\,(f(x)-L)=0,\] then \[\lim_{x\to a}\,f(x)=L.\]

Answer: 

It is true that if \[\lim_{x\to a}\,(f(x)-L)=0,\] then \[\lim_{x\to a}\,f(x)=L.\]

SAMPLE SOLUTION

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Solution: 

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What we are wanting to prove is that for every <Sign in to see all the formulas> there exists a <Sign in to see all the formulas> such that, if <Sign in to see all the formulas>, then <Sign in to see all the formulas>. Since <Sign in to see all the formulas> then this is automatically true given that

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