anonymous
  • anonymous
Find the limit L. Then use the ε-δ definition to prove that the limit is L. Lim (-5) x->4
Calculus1
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
What exactly is the limit? Is it just \[\lim_{x\to4}(-5)~~?\]
anonymous
  • anonymous
If that's the case, it should be clear enough what the limit is, considering \(f(x)=-5\) is a constant function. To prove this limit, you have to show that for any \(\epsilon>0\), you can find \(\delta\) as a function of \(\epsilon\) such that \(|f(x)-L|=\color{red}{|-5-L|<\epsilon}\) if \(0<|x-4|<\delta\). The red inequality is the key to the proof. If you can determine \(L\), you're done. An easy proof for an easy limit.

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