MATH 360 Midterm: MATH 360 UPenn m360 pracExam 2
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Due monday, november 6, 2017: is the function f xq x uniformly continuous from r0, q r0, q?prove your assertion, let f xq be a continuously di erentiable function from r0, 1s to and assume that f 0q 0. 0 f xq 2 dx as follows: (a) first, explain why it is true, for each x. that. 2 (b) now use some famous inequality (ahem) on the right side to get. 0 u tq 2 dt (c) now integrate both sides of that inequality as x goes from 0 to 1 (note that the right side is a constant): prove that. In: let f be a continuous function on ra, bs. Prove that there exists a number x in ra, bs such that. X a f tq dt b x f tq dt: prove that cos x 1 1. 2 x2 for all x: suppose that.
