(2) Suppose ƒ is continuous on [a, b] with f(x) ≥ 0 for all x € [a,b]. If | f(x) dx = 0, show that f(x) = 0 for all x = [a,b].

Q: . For which x value(s) is f(x) = 1 + x x² + 2 continuous? Explain why.

A:

Q: Let f(x)= V x³ at the interval of [0,2] ; then , use the mean valune theorem to find c.

A:

Q: Prove that if f is a continuous function on a closed interval [a, b], then

A: We have to prove the given inequality for a continuous function on a closed interval [a,b].

Q: Sketch the graph of a function f such that f (x) ≥ 0 on [0, 1] and f (x) ≤ 0 on [1, 2], whose…

A: Consider the function Then and The graph of the function is shown below,

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

A: Part(a) The correct option is option A. Because in option A has the  question does not make an…

Q: . If f : (0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: See the detailed solution below.

Q: 6. Prove that f(x)=√x is continuous for all x ≥ 0.

A:

Q: Let f: X --> Y be a function, and let U be a subset of X.  (1) Prove or disprove that f maps X \ U…

A: