Use the definition of continuity and the properties oflimits to show that the function                _______                                                    f(x) = x √ 16- x2 is continuous on the interval [-4, 4]

Q: Apply Corollary 2 to the Intermediate Value Theorem. f is a polynomial and continuous everywhere.…

A: Given that, f(-3) = 170 > 0 f(-2) = -25 < 0 f(-1) = 2 > 0 f(0) = -1 < 0 f(l) = 2 > 0…

Q: Study the continuity of the following functions and show the process of how you tell if it is…

A: Here is the full solution for both Parts: To study the continuity of the functions provided in the…

Q: Determine where the function m(x) = x+1 (x-1)(x-4) is continuous. The function is continuous on…

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.