A Tibetan monk leaves the monastery at 7:00 am and  takes his usual path to the top of the mountain, arriving at  7:00 pm. The following morning, he starts at 7:00 am at the  top and takes the same path back, arriving at the monastery  at 7:00 pm. Use the Intermediate Value Theorem to show  that there is a point on the path that the monk will cross at exactly the same time of day on both days.

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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.