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Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 2.6: Limits at Infinity and Horizontal Asymptotes Okay, remember that are not real numbers, so we cant yet say lim x f ( x ) with a straight face. But wed like to be able to: this should, in fact, be equal to the quantity that f ( x ) approaches, for all values of x sufficiently large, provided there is such a number. Lets just make this a definition: Definition. Suppose that f ( x ) is defined for all x on some interval ( a, ). We say that = L if we can make f ( x ) arbitrarily close to L by taking any values of x sufficiently large. Examples. 1. lim x 1 x = , as demonstrated in the graph below: 2. lim x e- x- 10 100 = , since even though f ( x ) isnt defined for a long, long, long time, eventually the function takes on values arbitrarily small. Mathematica might help us plot this functions graph: 3. lim x sin( x ), on the other hand, . Why is this? We make a similar definition for limits at...
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