Given information: (a) ƒ is a function with domain R. (b) A formula for computing ƒ is not given, but it is known that lim f (x) = 11. (c) It is also known that f (9) = 11. Use the definition of continuity to verify that f is continuous at c=9.

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A:

Q: 8) Graph the function f:R → Z defined by f (x) = [;x]. Include everything that would fit on the…

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Q: Describe the interval(s) on which each function is continuous: f(x) =tan x

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Q: Determine whether the following function is continuous at a. Use the continuity checklist to justify…

A: We have to check

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A: Part (a) For the function to be continuous at x = 0, we should have Left hand limit (LHL) = f(0) =…

Q: 1. - Cos x x +0 f(x) = (0, %3D 3C

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A:

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.