MAT137Y1 Lecture 8: Definition of a Limit
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Date: january 22, 2020 assume that f(x) is defined on a punctured interval (c , c) (c, c + ), where > 0 represents a small distance to the left and right of x = c. If lim f(x)=l and lim f(x)=m, then l=m. A limit lim f (x) exists if it is equal to some real number l. if a limit exists, then it can be equal to one and only one number. The left limit lim f(x) = l means that for all > 0, there exists > 0 such that if x (c , c), then f (x) (l , l + ). The right limit lim f(x) = l means that for all. > 0, there exists > 0 such that if x (c, c + ), then f (x) (l , l + ). For a limit to exist, the left and right limits must.
