MTH 207 Final: MTH 207 Final Exam Fall 2004

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31 Jan 2019
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You are allowed to use one letter-size (a4) two-sided formula sheet. You may not use calculators or other electronic devices. Marks for each question are indicated by [ ]. Give full justi cation for your answers; the correct answer alone may be worth nothing. The following table is for the instructors" use only; please do not write anything in the empty boxes next to the question numbers. [9] (1) find the following limits, if they exist, or explain why they do not exist: (a) lim x 1 (x 1)(x3 + 3) 2y2 + y (c) lim x 1 x ln x sin( x) [9] (2) find the derivatives dy dx of the following functions: ex (a) y = 1 + x2 + tan(ln(2x)). (b) sin(xy) = x2 y. (c) f (x) = z ex. [6] (3) use logarithmic di erentiation to nd the derivative of (2 x)5 x + 1 (x + 3)7 y =

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