3. In your solution to this problem, specify exactly where (if anywhere) you're using a limit law/theorem. Knowing that cos is continuous (at every point), show that lim sec x exists at every c such that cosc + 0. Find the limit for such c and deduce that the function sec is continuous at every point of its domain. In fact, the same is true for each of tan, cot, csc as well (but you do not have to show this).

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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.