Determine whether the following statements are true and give either an explanation or a coun- terexample. 1 = lim 22 2x x – 2 1 (a) By L'Hopital's Rule lim 1-2 x² – 1 (b) lim r sin r = lim f(x)g(x) = lim f'(x)g'(x) = (lim 1)(lim cos x) = 1 (c) The number 1 raised to any fixed power is 1. Therefore, because (1+ x) →1 as r→ 0 then we have that (1+ x)/= →1 as x → 0.

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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.