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# practicefinal - BAv-v 45” ‘3 MATH 3 EARLY FINAL...

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Unformatted text preview: BAv-v 45” ‘3 MATH 3 EARLY FINAL 1217/2004 lnstructor: Frank Béiuerle, Ph.D. No books, graphing utilities or notes allowed. Show your work. Show your work. Show your work. YourName: Your TA: Max Your score Problem 1: 10 Problem 2: .10 Problem 3: 15 Problem 4: 10 Problem 5: 10 Problem 6: 10 Problem 7: 10 Problem 8: 20 Problem 9' 10 Problem 10: 20 Problem 11: 15 Problem 12: 20 Problem 13: 15 Problem 14: 10 Problem 15: 10 Extra Cr 16: 10 TOTAL: 205 Relax, good luck, have a great winter break. 1. ( 10 points) Use the reference angle principle to get the exact value of the following: (a) sin 225° on com 3 ) 2. (10 points) Give a table that gives the exact values AND decimal approximations, rounded to the nearest hundredth, for sin 0,0080! and tana for a z 0°,a = 30°, 0: = 45°,a = 60° and a = 90°. Also give the radian measures of all the angles. 1 . 3. (15 points) Consider the function f(;1:) = 2 005(22: + Find the followmg: (a) (1 points) The amplitude of f. (b) (2 points) The period of f. (c) (2 points) The phase shift of f. (d) (5 points) The graph of f. . 1 . . (e) (4 pomts) Now graph 9(2) 2 2 sec(2\$ + Into the same coordlnate system above. 4. (10 points) Give the exact values of the following by using (and drawing !) the appropriate triangles: (a) oosIsin*‘(—§)1 (b) sin [arctan(2)] 5. (10 points) Graph f = arctan(\$) + 1. Make sure to label all asymptotes. (Extra Credit, 2 points) Use your graph to graphically ﬁnd/ estimate the solution(s) of the equation arctan(x) + 1 == 1. What are the exact values of all solutions '2' d1 6. (10 points) Find all Solutions for the following equations: 1 t = ~ (a) an x 2 (h) sinzz+3inz-6=O 7. (10 points) A vertical ﬂag pole is on the ﬂat roof of a building. From a. point on the ground 50 feet away from the building, the angles of elevation to the top and the bottom of the ﬂag are 15° and 12° respectively. Find the height of the ﬂag. 8. (20 points) Consider the function f(:c) = 111(x + 1) (a) (5 points) Show that the function f(x) is one’to-one. (You can do this algebraically or graphically) (b) (5 points) Find f‘1[:c). (c) (10 points) Graph both ﬁx) and f‘1(x) in the same coordinate system. 9. (10 points) 200kg of a radioactive substance with a half-life of 20 years is held in a storage container. How long must one wait until only 2 kg of the substance is left ? Hint: First use the half-life T to compute k for which you can use the following half-life l formula: k 2 —-—112. T 10. (20 points) Give all real solutions to the following equations. (a) logso + 1) = 2 (13) 21113:: 1+ln(x+1) (c) 62” + 23” + 1 = 0 Hint: Rewrite eh appropriately to factor as a. trinornial (d) lnlnlnx = 0 11. (gpoints) a) Two numbers add up to 33. Find the maximal value for the product of these two numbers. b) Two non-negative integers add up to 33. Find the maximal and the minimal value for the product of these two numbers. 12. (20 points) Let 0 be an angle such that 7r 5 0 5 33“- and sin!) 2 —§. Find the following: (a) (2 points) tanB = (b) (2 points) cost? = (c) (2 points) cot 0 = (d) (2 points) sect? = (e) (2 points) cscB = (f) (3 POintS) 605(29) = . 3 . . . . (g) (3 points) Is cos( posﬂuve or negatwe? Explam. (h) (4 points) 3 = calculator and your brain here) in degrees and radians (you should use your 10 ‘5 ' :62-—3:c——4 13. (23 points) For the rational function = m do the following: (a) Find all m-intercepts (if any). (1)) Find the y—intercept. (c) Find all vertical asymptotes (if any). ((1) Find the horizontal asymptote. (e) Where does the graph intersect the horizontal asymptote ? (f) Sketch the graph (label the axes, asymptotes and all intercepts): 11 14. (10 points) Let a = 7, a := 40° and b = 9. Find one solution of this triangle. (Extra Credit, 5 points) Find the other solution. 12 15. (10 points) 3) Find an equation of the sine function with the following graph: 1)) Give a reason Why the following graphs. cannot represent a polynomial function with highest degree term —:c5. - ‘0 13 N 16. (Extra Credit, 10 points) Let a sequence be deﬁned by an“ =an+2,a1 = l,n=l,2,3,... (a) Find the next three elements «12, a3, (14 of this sequence. 0200 (c) Find an eicplicit formula for an. (d) What is the value of the sum of the ﬁrst n elements of the sequence, namely What is the sum ' 1" K: r+1+s+-,,+(n—r)+ n Kai 14 IT ...
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practicefinal - BAv-v 45” ‘3 MATH 3 EARLY FINAL...

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