MTH 207 Final: MTH 207 Final Exam Fall 2005
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You are allowed to use one two-sided 8. 5 11 formula sheet. Marks for each question are indicated by [ ]. Give full justi cation for your answers; the correct answer alone may be worth nothing. [8] (1) find the following limits, if they exist, or explain why they do not exist: (a) lim x 0. |x|(x2 + 3) x (b) lim y 2 y2 5y + 6 y2 4 (c) lim x 0 sin(5x) [8] (2) find the derivatives dy dx of the following functions: (a) y = 3e x + 1. 3 x2 e tan 1(x). (b) x3 + y3 = 3x2y. (c) y =z cos(x) [5] (3) use logarithmic di erentiation to nd the derivative of y = 3s x 2 (x2 + 1)(2x + 3) [15] (4) evaluate the following de nite and inde nite integrals: (a) z 1 + cos2(x) cos2(x) dx. (b) z x. 1 + x2 dx. (c) z e2 e.
