MTH 207 Midterm: MTH 207 Midterm 2006
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No aids are allowed, including no calculators and no formula sheets. Marks for each question are indicated by [ ]. Give full justi cation for your answers; the correct answer alone may be worth nothing. [16] (1) (a) de ne the function f (x): Find the domain of f (x): f (x) = Find the inverse function f 1 of f : 1 (b) simplify sin(arctan x) (c) evaluate e3 ln(2) ln(4) If a limit does not exist, explain why. (a) lim x x . X2 + 1 (b) lim x 2 (x + 1)|x + 2| x + 2 (c) lim x . 4x6 + x x3 2 (d) lim x 1. X2 + 8 3 x + 1. [8] (3) find all asymptotes (vertical and horizontal) of the curve y = x3 + 1 x3 + x. Explain your reasoning. x6 cos(1/x2) = 0. lim x 0.
