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154 prerequisite quiz solutions

154 prerequisite quiz solutions - MTH 154 Prerequisite Quiz...

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Unformatted text preview: MTH 154 Prerequisite Quiz Name kg :2; Fall 201 l Directions: Work each problem. You should be able to complete this quiz in 30 minutes. Do not use calculators, notes, texts, or other people. Each of the problems is typical of what you will be expected to do in solving calculus problems with all of the calculus removed. Then grade the quiz using the solutions posted on moodle. Do not look at the solutions before working the problems. There is no partial credit. If your score is below 7, take this to be an indication that you need to periodically review algebra and trigonometry while taking calculus. 1. The graph of a function f is shown. Find (or rather estimate) all solutions of the inequality f (x) < 2 . State your approximate solutions as an interval or a union of intervals. /”_—_// “in, r F F“ \\\ W Solutions: Q ‘ 3 - S > I 3 / \_p / -\ » \. /, <-\...~,__‘__._, W...» »~ - *' " "A ‘ ”‘TMH" ' “‘“Mn.m_ww/ 2. Find all solutions of the equation: 2 + ex—1 appropriate functions. vy _ \ 3 'X - \ I (M H E) : I \ /"~’/\J N-i (“All ( NC: |—+(«|l =13 . Leave your solution(s) in terms of Y m a,“ 3. Find all solutions of the equation below that are in the interval [0, 2n]: 2 cosx —1 = O . (Of course, the measure for the trigonometric functions is radian measure.) ‘/ Cogmi i; pomM-M a, COS”! = 3 T9") W ‘ Tr a _ _. 3 . 7 17‘ 9| — 5’3 :. 5/ 4. Solve the following literal equation for D in terms of x and y: x — 2D = xy—f yD— 2x. 5. Write the expression below in terms of ln(x— 1), ln(x +1), and ln(x2 +1). That is, the only appearances of the natural logarithm function are these three. // M I 3 " |+3K(’X~I\~)(M{’X+I\-‘3Lu(’x-H For problems 6 and 7, use the diagram shown to the right. 0 7. l b 6. Express b as a fimction of c. (That is, b should be equal to an expression where the only variable in the expression is c.) @aék @wkamw mew”, (44 7 : c 7. Express b as a function of 0. USA 49V hiWfiN Jnncfl’btr‘v‘ 41nd- id's/WW“ Cl '1: +°Hna 8. Identify which of the following are true for all positive values of x and y. Write the appropriate letters in the blank below. More than one can be true, and none can be true. If none are true, write “none.” Mala Suv W (a) a'b_2=b—2 (d) Eli=1nx—1ny stw ml , a my Q . l'}. C , J at” d. l (b) 1n(x+y)=1nx+1ny (e) (ex)’=exy (.er 3 ‘ (c) sin(2x)=2sinx True Items: { e) 2 9. Let f(x) = 5 —(x2 —1)sin(x2 —1)+ \/2(x2 —1) —ex ‘1. Find a function g(x) for which f(x) = g(x2 —1). l:i 3([:\: S— I: 3&‘2 "' \IDQ - '6 y 30:0: S-'xsi~xly+\l3~ -€ 10. A rectangular yard lies along a long straight building. The yard is to be fenced by 800 feet of fencing material. This includes the boundary of the yard (not including the side along the building). Express the total area A of the yard as a function of the length x of the side perpendicular to the building. Extra Credit (1 pt): Find the domain of the function in problem 10. That is, find the set ~.\ of all values of x for which the areaA makes physical (and common) sense. I "\ Lnréxfl y '- Smailda‘ 3" l" ONO“; \ a .‘\ O (V‘J- mol\ 2 (0’ “00) 8‘00 - 9*: V Smallaié 4! .v C) (“c+ vkglmp.w\ ’XT‘JOO ...
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