MATH137 Study Guide - Midterm Guide: Intermediate Value Theorem, Liquid Oxygen, Binary Logarithm
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MATH137 Full Course Notes
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Note: only answers (and some proofs) are contained here. whenever x > 1 (b) at a height of 2km the barometric pressure is changing at a rate of 1 kilopascal per km. (c) tanh x = ex e x ex + e x . Thus, by the intermediate value theorem there exists a root of f between. 3x2 sin (cid:20) (b) lim x 0 (c) lim x 0. Cos x sin x cos2 x sec(x2 + x) tan(x2 + x)(2x + 1)(3e2x + 1) 6e2x(sec(x2 + x)) (3e2x + 1)2. 2 (cid:18: x = k , cos sin 1. 3: f (x) is continuous on ( , 1) (1, ). (a) show that sinh 1 x = ln(x + Then, x2 + 1) ey e y x = sinh y = Then, by the quadratic formula we get ey = Since, ey 0 we must have and so y = ln(x +