MATH111-200630-MT01 - UNIVERSITY OF REGINA DEPARTMENT OF...

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Unformatted text preview: UNIVERSITY OF REGINA DEPARTMENT OF MATHEMATICS AND STATISTICS MATH 111002 200630 Midterm Test 1 Time: 50 minutes Instructor: Dr. Edward Doolittle Name: Student #: Section: You have 50 minutes to do each of the following questions. The test is worth a total of 50 marks. Non-programmable calculators, logarithm tables, and/or slide rules are permitted; no other aids are permitted. Use the backs of the pages for rough work. 1. (10 marks) Find the following derivatives: (b) (5 marks) y where y (a) (5 marks) y where y eln x xe (x to the power of e to the power of x) x 2 Page 1 of 4 MATH 111002 200630 Midterm Test 1 Time: 50 minutes Page 2 of 4 Name: Student #: Section: 2. (10 marks) Find the following integrals: (a) (5 marks) ex 1 0 (b) (5 marks) x3x dx 2 (a) (2 marks) Find f x . 3. (10 marks) Let f x x ex e x dx x for x 0. MATH 111002 200630 Midterm Test 1 Time: 50 minutes Page 3 of 4 Name: Student #: Section: (c) (2 marks) Show that f is invertible. (e) (2 marks) Find f 4. (10 marks) Use logarithmic differentiation to find the following derivatives. (a) (5 marks) f x where f x (d) (2 marks) Find f 1 6. 1 6. xex x2 2 (b) (2 marks) Show that f x 0 for all x 0. 1 10 MATH 111002 200630 Midterm Test 1 Time: 50 minutes (b) (5 marks) y where xy Page 4 of 4 Name: Student #: Section: 6 e 5. (5 marks) Find dx . x ln x 6. (5 marks) Show that if f is twice differentiable and increasing, f # !! # " ! yx , x y 0 1 x f f 1 x f f 1 x 3 . ...
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