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

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

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

Answer: 

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

SAMPLE SOLUTION

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Solution: 

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