Transcription of Lecture 4 : Calculating Limits using Limit Laws
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Lecture 4 : Calculating Limits using Limit Laws
Lecture 4 : Calculating Limits using Limit LawsClick on this symbolto view an interactive demonstration in Wolfram the definition of the Limit , limx af(x), we can derive many general laws of Limits , that help us tocalculate Limits quickly and easily. The following rules apply to any functionsf(x) andg(x) and alsoapply to left and right sided Limits :Suppose thatcis a constant and the limitslimx af(x)andlimx ag(x)exist (meaning they are finite numbers).Then1. limx a[f(x) +g(x)] = limx af(x) + limx ag(x) ;(the Limit of a sum is the sum of the Limits ).2. limx a[f(x) g(x)] = limx af(x) limx ag(x) ;(the Limit of a difference is the difference of the Limits ).3. limx a[cf(x)] =climx af(x);(the Limit of a constant times a function is the constant times the Limit of the function).4. limx a[f(x)g(x)] = limx af(x) limx ag(x);(The Limit of a product is the product of the Limits ).
(c) Determine the in nite limit (see note 1 above, say if the limit is 1, 1 or D.N.E.) lim x!2 x+1 (x 2). Polynomial and Rational Functions Please review the relevant parts of Lectures 3, 4 and 7 from the Algebra/Precalculus review
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