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).
the graph, y= c). 8.lim x!ax= a, (follows easily from the de nition of limit) 9.lim x!ax n= an where nis a positive integer (this follows from rules 6 and 8). 10.lim x!a n p x= n p a, where n is a positive integer and a>0 if n is even. (proof needs a little extra work and the binomial theorem) 11.lim x!a n p f(x) = n p lim x!af(x) assuming that ...
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