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How-To Calculus Limit Limit from the Left Limit from the Right One-Sided Limit

Evaluating One-Sided Limits from a Graph

Author: ShaNisaa RaSun

The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Answer" to reveal the answer to the problem.

Problem: Using the graph of \(f\) shown below, estimate the following limits, if they exist.


A graph of a piecewise function f with holes when x=-4 and x2 and the limit does not exist when x=-7

  1. \({\displaystyle \lim_{x\to -7^-} f(x)}\)
  2. \({\displaystyle \lim_{x\to -7^+} f(x)}\)
  3. \({\displaystyle \lim_{x\to -4^-} f(x)}\)
  4. \({\displaystyle \lim_{x\to -4^+} f(x)}\)
  5. \({\displaystyle \lim_{x\to 0^+} f(x)}\)
  6. \({\displaystyle \lim_{x\to 2^-} f(x)}\)
  7. \({\displaystyle \lim_{x\to 2^+} f(x)}\)
  8. \({\displaystyle \lim_{x\to 5^-} f(x)}\)

  1. \({\displaystyle \lim_{x\to -7^-} f(x)=-2}\)
  2. \({\displaystyle \lim_{x\to -7^+} f(x)=2}\)
  3. \({\displaystyle \lim_{x\to -4^-} f(x)=2}\)
  4. \({\displaystyle \lim_{x\to -4^+} f(x)=2}\)
  5. \({\displaystyle \lim_{x\to 0^+} f(x)=0}\)
  6. \({\displaystyle \lim_{x\to 2^-} f(x)=2}\)
  7. \({\displaystyle \lim_{x\to 2^+} f(x)=2}\)
  8. \({\displaystyle \lim_{x\to 5^-} f(x)=5}\)

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