MATH 1500X Final: MATH 1500 Final Exam
31 Jan 2019
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How to prepare for the nal: the most e ective way is to go over the problems, especially on homeworks, review sheets and midterms, please attempt the problems before looking up the answers. Remember: you learn by doing; math is not a spectator sport! Sketching of functions (including things like xx = ex ln x) Related rates: this includes problems involving trig functions, similar triangles etc. Exponential growth / newton"s law of cooling: linear approximations including error bounds, newton"s method. Some additional review questions: continuity and limits: . repeat, but replace 0. 1 by . (a) state delta-epsilon de nition of continuity. Find such that (cid:12)(cid:12)x2 4(cid:12)(cid:12) 0. 1 whenever |x 2| < (b) show that a step function f (x) = (cid:26) 0, x 0. 1, x > 0 (c) show that the function f (x) = (cid:26) sin 1 x , x 6= 0.
