Define if t <5 at + +1 if T sin t h(t) = + 1 Show that h(t) is continuous for all t. Show that h(t) is NOT differentiable for all t. In particular, show that h(t) is differen- tiable at t = 7 but NOT differentiable att = T.

Q: 1. Show that the function, defined for x E R by f(x) = 1 is uniformly continuous 1+x² on R.

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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.