MATH 151 Midterm: MATH 151 TAMU Y2014 2014c X3combo
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Then: (a) draw a right triangle with = tan 1(cid:0) 1. = 1: (e) recall that the cosine function has period 2 . 0 quotient gives x 0(cid:0) 3(cid:0)1 + x2(cid:1)(cid:1) = 3: (b) now f (x) = 1 + x 2 implies f (x) = x x 1 +c, + xe 2x2: (a) now f (x) = 1 e 2x2. 2(cid:1): (b) solve f (x) = x3 + x2 = x2 (x + 1) = 0 to obtain. 2 ; f is increasing on (cid:0) 1: (c) now f (x) = 1 2 cos x < 0 where cos x > 1. 3(cid:1): (d) now f (x) = x4 x2 = x2 (x 1) (x + 1) = 0 for x = 1, 0, 1. These are the x-coordinates of the in ection points: (a) let y = (tan x)sin x.
