Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones

      In this chapter, you encounter a variety of problems involving limits:

       Using graphs to find limits

       Finding left-hand and right-hand limits

       Determining infinite limits and limits at infinity

       Practicing many algebraic techniques to evaluate limits of the form 0/0

       Determining where a function is continuous

What to Watch Out For

      You can use a variety of techniques to evaluate limits, and you want to be familiar with them all! Remember the following tips:

       When substituting in the limiting value, a value of zero in the denominator of a fraction doesn't automatically mean that the limit does not exist! For example, if the function has a removable discontinuity, the limit still exists!

       Be careful with signs, as you may have to include a negative when evaluating limits at infinity involving radicals (especially when the variable approaches negative infinity). It’s easy to make a limit positive when it should have been negative!

       Know and understand the definition of continuity, which says the following: A function f(x) is continuous at a if .

Finding Limits from Graphs

       167–172 Use the graph to find the indicated limit.

      167.

      168.

      169.

      170.

      171.

      172.

Evaluating Limits

       173–192 Evaluate the given limit.

      173.

      174.

      175.

      176.

      177.

      178.

      179.

180.

      181.

      182.

      183.

      184.

      185.

      186.

      187.

      188.

      189.

      190.

      191.

      192.

Applying the Squeeze Theorem

       193–198 Use the squeeze theorem to evaluate the given limit.

      193. If for all x in , find .

      194. If for , find .

      195. If for , evaluate .

196. Find the limit: .

      197. Find the limit: .