Suppose f and g are continuous on [a, b] and f f(x) dx = S% 8(x) dr. Prove that there is cE [a, b] such that f(c) = g(c).

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A: We have to evaluate by Green's theorem.

Q: the function f is not differentiable at x=0.

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Q: (6) Are all continuous functions on ID differentiable on D?

A: we have to identify the given statement is true or not

Q: Please

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A: This question is based on Rolle's theorem which is explained in step 2.

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Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

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.