MATH 32 Study Guide - Final Guide: Binary Logarithm, Liquid Oxygen, Polynomial Long Division
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Math 32 fall 2013 final exam solutions (1) (12 points) evalute the following (a) tan(0) 8 ), we"ll use the half angle formula: . 8 is in the rst quadrant, so its sine is positive. Solution: ln((e2)(e3)) = ln(e2+3) = 5. (d) log2(sin( . So for x to be in the domain of g, we must have x2 > 0. In fact, x2 0 for all x, with x2 = 0 only when x = 0. So the only problem occurs when x = 0. The domain of g is all real numbers except 0, or, in interval notation, ( , 0) (0, ). (b) (3 points) what is the domain of h? de ned) and 1 ln(x) 0 (so that(cid:112)1 ln(x) is de ned). Solution: for x to be in the domain of h, we must have x > 0 (so that ln(x) is inequality, 0 1 ln(x) ln(x) 1 eln(x) e1 x e.
