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.
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Evaluating Limits
173–192 Evaluate the given limit.
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Applying the Squeeze Theorem
193–198 Use the squeeze theorem to evaluate the given limit.
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196. Find the limit:
197. Find the limit: