Actual Midterm 2 Solutions - Solutions Midterm Exam 2 Apr 6 2015 1(a(10 points State the intermediate value theorem for continuous functions A

Actual Midterm 2 Solutions - Solutions Midterm Exam 2 Apr 6...

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Solutions Midterm Exam 2 — Apr. 6, 2015 1.(a) (10 points) State the intermediate value theorem for continuous functions.A continuous functionfon a closed interval [a, b] assumes all values betweenf(a) andf(b).(b) (15 points) Letf: [0,1][0,1] be continuous. Show that there is at least onex[0,1] so thatf(f(x)) =x.Consider functiong(x) =f(x)-xthis function is continuous asfis as well. If
Math 405, Fall 2015 Solutions to Midterm Exam 2 — Apr. 6, 2015 Page 2 of 4 2.(a) (10 points) Give the formal definition for a functionf:DRto be uniformly continuous.

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