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Lecture

# Mock-Ma129-Fin-s11.pdf

9 Pages
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School
Wilfrid Laurier University
Department
Mathematics
Course
MA129
Professor
Shane Bauman
Semester
Winter

Description
MA129 Mock Final Name: Time Allowed: 120 minutes Total Value: 85 marks Number of Pages: 9 Instructions: Cheat Sheet: One 8:5" ▯ 11" page of study notes (both sides) is allowed as a reference while completing the mock test. Please note, that the cheat sheet is permitted for the mock test only! Non-programmable, non-graphing calculators are permitted. No other aids allowed. Check that your test paper has no missing, blank, or illegible pages. Note that test questions appear on both sides of the paper. Answer in the spaces provided. Show all your work. Insu¢ cient justication will result in a loss of marks. 1. [2 marks] Solve the equation for x: 43x+1 = 16 2x▯5 2. [5 marks] Solve the equation for x: log2(x ▯ 4) = 3 ▯ log2(x ▯ 2) 1 ▯ 2 ▯ ln x ▯ 4 3. [3 marks] Determine the domain of the function f (x) = x + 5 . Express your answer using interval notation. 2 4. [4 marks] Determine the equation of the line tangent to the curve y = f (x) = lnx + x at x = 1. Express your answer in the form y = mx + b. 5. [2 marks] Determine the derivative of the function: g (x) = x log (3 ▯ x) 4 00 2x+1 ▯ 3 ▯1=3 6. [4 marks] Determine y given: y = 3 + 2x ▯ 1 2 7. [6 marks] Suppose you own an apartment building containing 100 uniIf you charge \$400 per month for each unit, then all units can be rentedFor every \$20 increase in monthly rent, you will lose one customer. What monthly rent should you charge to maximize your revenue? Show that the corresponding revenue is an absolute maximum. 8. [3 marks] Given the following matrices, 2 3 " # " # 2 1 3 ▯1 2 1 0 1 4 5 A = 0 1 4 B = 0 1 1 C = 0 ▯1 , 1 0 determine (A ▯ 2B)C. 3 2 2 x 0 x ▯ 4x 00 8 9. [9 marks] Let f (x) = x ▯ 2 . Then f (x) = 2 and f (x) = 3. (x ▯ 2) (x ▯ 2) (a) State the intervals on which f is increasing and those on which f is decreasing. (b) Determine the coordinates of all relative maximum points and relative minimum points. (c) State the intervals on which the graph of f is concave up and those on which it is concave down. 4 Z 4 2 x + 3x ▯ 4 10. [2 marks] Evaluate the integral: x2 dx Z ▯ ▯ 1 x e x e+1 11. [2 marks] Evaluate the integral: + ▯ x + e ▯ 2 dx x e R p 12. [4 marks] Evaluate the denite integral: x2 3x + 1 dx 0 Z
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