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Calculus/Proof of limit

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Question
lim x→a f(x)= L Prove that  lim x→a [f(x)−l]=0 Prove it with delta and epsilon

Answer
Let e be epsilon and d be delta.

If we know that lim x→a f(x)= L, then for any x within (a,a+e),
it is known that f(x) < Ląd.  

When L is subtracted from each term in the inequality, the result is f(x) - L < ąd.

That is the what is needed to prove that lim x→a [f(x)-L] = 0.  

Calculus

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