lim x = 9 [Hint: Write |x² – 9|= |x + 3||x – 3|. Show that if |x – 3|< 1, then |x + 3| <7. If you let 8 be the smaller of the numbers 1 and e/7, show that this 8 works.]

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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.