Problem 1.Show that if ƒ is continuous on an interval I, then for any a, b, c E I,| S(t)dt +f(t) dt= | f(t)dt.aHint: Assume a < b and consider the four cases: c = a,c =b, с <а b or a = b.

We have to prove given expression.

Answered: Problem 1. Show that if f is continuous…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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x 1 -2 3 Continuous at x=1
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Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) = 10 x over the interval [10, 10]. In other words, find c E [10, 10] such that f(c) This function has two values, c₁ and c₂, where c₁ < C₂. 41 = 10 10-11-10) / 10 -10) / f(x)dx. - 10 - C2
Does the function satisfy the hypotheses of the Mean Value Theorem on the given Interval? f(x) = x3 + x - 6, [0, 2] O Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on R. O Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. O No, f is not continuous on [0, 2]. O No, fis continuous on [o, 2] but not differentiable on (0, 2). O There Is not enough information to verify if this function satisfies the Mean Value Theorem. If it satisfles the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers hypotheses, enter DNE).
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Problem 1. Show that if f is continuous on an interval I, then for any a, b, c E I, | ()dt + f(t)dt. Hint: Assume a < b and consider the four cases: c = a, c = b, c < a < b, a < b < c. (The case a b or a = b.