Consider the transport equation ut 2ux, u(0, x) = f(x), where J cos+1 if |x| < T f (x) = otherwise. Given any t > 0, find the interval I such that u(t, x) # 0 for all x E I

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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.