1. Suppose that lim-7g(x) 6 and X->-7 2f (x)4 1, 3g(x) lim x--7 use the limit properties theorems to (a) justify that lim-7 f(x) exists and (b) find the value of lim-7 f(x) :-+-7 Hint: As we discussed in lecture, the limit properties do NOT justify writing 2 lim-7 f(x)lim74 3 limg7g(x) ;->-7y in this instance.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.