Which of these is a conclusion of Rolle's Theorem? Select all that apply. There is a number c in the open interval (a, b) such that f'(c) = {f(b) - f(a)} / (b - a). There is a number c in the open interval (a, b) such that f'(c) = 0. There is a number c in the closed interval [a, b] such that f(c) = 0. fis constant on the closed interval [a, b]. fis constant on the open interval (a, b).

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A: To show that there does not exist a function f(x,y)

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Q: 5. If f is continuously differentiable on (0, 1] and f(1) = f (0) = -1/6, prove that dr 22 2 Hint:…

A: Continuously Differentiable Function: A function f is continuously differentiable on [0, 1] if its…

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Q: 5. Define f : (0, 1) → R by f(x) = x+1 Can one define f(0) to make f continuous Vx at 0? Explain.

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

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Q: B) Let f:[-2,2]R. then show that the function xsin -) for x 0, f(x) = for x = 0, is uniformly…

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A: we have to find

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A: topic - derivative of a function

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Q: 8. Let f,g be differentiable on R and suppose that f(0) = g(0) and f'(x) 0. Show that f(x) 0.

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Q: 7. Find a and b such that f is differentiable everywhere. f(x) = {+b, S ax³, lx² + b, x 4

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Q: Prove Fermat’s Theorem for the case in which f has a localminimum at c .

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Q: Which of the following is true about f(z) = z+ iz %3D 22 ختر أحد الخيارات to Neither Continuous nor…

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Q: 3. Let (1) be defined by >-{b ²2. Osi<1. 15152, 16-1², and let F(x) be defined by F(x)=f() dr. 0sx=2…

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Q: 2. Prove that if f: I R is continuous on I, then |f|: I – R where |F(x) := |f(x)| Vz E I is…

A: f is defined on the set of real numbers. The detailed solution is as follows below:

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Q: (1) Give an example of a function f such that | f |is Riemann integrable but f is not.

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Q: Let I be an interval disjointed from (-1,1) Prove that the function f(x) = x + (1/x) is increasing…

A: Solution: Consider the given function is: f(x) = x + 1x    ...(1) Also, the given interval Let I is…

Q: 2. Let r E R. Let f: [0, 0) → R be a function defined by f (x) = - for all x € (0, 0) and f (0) = r.…

A: For the solution of the problem follow the next step.

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Q: Determine where h(x) = sin(x- Sx + 2) is continuous. %3D h is continuous on the interval [0, co). h…

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Q: 3. Let f(r) = 8 – 4x4/5. Carefully explain why f is continuous on [-1, 1), f(-1) = f(1), but there…

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Q: Identify the open intervals on which the function is increasing or decreasing. (Select all that…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.