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The Squeeze Theorem - UCLA Mathematics

Math 31A Discussion SessionWeek 2 NotesJanuary 12 and 14, 2016 This week we ll discuss a powerful tool for computing limits, called the Squeeze theo-rem. Following this, we may also mention limits at infinity, whose computation sometimesrequires different methods. Finally, we will give a geometric motivation for the derivative,and investigate some of its Squeeze TheoremAs useful as the limit laws are, there are many limits which simply will not fall to thesesimple rules.

Limits at In nity We’ll carry out two illustrative examples of limits at in nity. Example. 1.Find lim x!1 8x5 + 3x2 4 4 9x5, if it exists. (Solution)Neither lim x!1(8x5 + 3x2 4) nor lim x!1(4 9x5) exists, so we cannot very well consider a ratio of these limits. What we can do, however, is rewrite this

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