MAC 2312 Lecture 11: Lectures 11-20
16 Dec 2017
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2x2 + x 1 : factor and reduce the expressions, then plug in the x value. ex. Let f, g, h be functions satisfying f (x) g(x) h(x) for all x near a, except possibly at x = a. If then lim x!a lim x!a f (x) = lim x!a g(x) = l. h(x) = l, Note: since lim cos(1/x) does not exist , x!0 the basic limit law can not be used. But we know | cos x| 1, hence. X2 x2 cos# 1 x$ 1 x$ x2 ( x2) = 0 lim x!0 x2 = lim x!0 for x 6= 0 for x 6= 0. We apply the squeeze theorem to con- clude that x2 cos 1 x = 0 lim x!0. L11 - 4: the basic limit laws: [f (x)]p/q = lim npf (x) = nqlim x!a x!a f (x) p/q. , q 6= 0 f (x), n positive inte- ex. lim x!0 sin2 x x.
