(a) State (without proof) the extreme value theorem.(b) Give an example of a function ƒ : [0, 1] → R that is not bounded. (c) Let ƒ : [−1,1] → R be a continuous function. Prove that the sequence (n)defined inductively by1ΧηXn+1 = xn+2₂m² (₁ + [x₂]:·), x₁ = 0,X1

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Answered: (a) State (without proof) the extreme…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Let f be the function whose graph is given below. (a). Use this graph to find the largest number &> 0 such that if 0 0 such that if 0 < x-4 <8 (Enter dne if no such & exists.) 8= dne then f(z)-4) <3. then f(x) - 4 <0.8.
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(a) On what open intervals contained in −1<x<3 is the graph of f concave up? Give a reason for your answer. (b) Does f have a relative minimum, a relative maximum, or neither at x=1 ? Justify your answer. c) Use the Mean Value Theorem on the closed interval [−1,1] to show that f′(−1) cannot equal 2.5. (d) Does the graph of f have a point of inflection at x=0 ? Give a reason for your answer. need help on all
uploa... Sy 10- (a) Locate all the local minima of f(x). Briefly justify your answer. (b) State the interval(s) in which f is concave down. Briefly justify your answer. 3. Consider the function x5 + x? 20 f (x) = e-* - (a) Use the Intermediate Value Theorem to show that there is one point x = a such that f"(a) = 0. (b) Prove that there is only one point for which f"(a) = 0 [Hint: look at the third derivative]. Is this an inflection point? Explain. (c) Assume that f"(x) > 0 for x a. What does the first derivative test (applied to f) say about f'(x)? (d) Use the result obtained in part (c) to determine the number of critical points of f. 1. A right circular cylinder of height h 2x is inscribed in a sphere of fixed radius R.

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(a) State (without proof) the extreme value theorem. (b) Give an example of a function ƒ : [0, 1] → R that is not bounded.