Transcription of The Squeeze Theorem - UCLA Mathematics
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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. One helpful tool in tackling some of the more complicated limits is theSqueezeTheorem: Theorem ,g, andhare functions so thatf(x) g(x) h(x)neara, with the exception that this inequality might not hold whenx=a. Thenlimx af(x) limx ag(x) limx ah(x),if these three limits exist. In particular, if limx af(x) =L= limx ah(x), thenlimx ag(x) = Evaluate the limit limx 0(x cos(1/x)), if it exists.(Solution) We know that 1 cos(1/x) 1 for allx6= 0.
The Squeeze Theorem As useful as the limit laws are, there are many limits which simply will not fall to these simple rules. One helpful tool in tackling some of the more complicated limits is the Squeeze Theorem: Theorem 1. Suppose f;g, and hare functions so that f(x) g(x) h(x) near a, with the exception that this inequality might not hold ...
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