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.
This ts with our understanding of the derivative as an instantaneous slope, since the graph of a constant function is a horizontal line. Because it is de ned as a limit, the derivative also has the following pleasant arithmetic properties: Proposition 2. Suppose f0(x) and g0(x) exist and c;dare real numbers. Then 1. d dx (cf(x) + dg(x)) = cf0(x ...
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