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Test%201 - V 2 September 2000 Teaching Assistant f i Hour...

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Unformatted text preview: V 2] September 2000 Teaching Assistant f i - Hour TestI Math 15011-1 Andrew Instructions: 1. Closed book, calculators may be used. 2. Show your work and explain your answers and reasoning. 3. Express your answers in simplified form. 1. (25) Evaluate the limits 5 ‘ '-« i. i ' ' .. x'—2x—3 l“ “ / a. lim-—-—-—fi - r ' 143A" — 4x + 3 r - : - 5 . tan(2x) 3m?“ ‘ b. 11m >uw~~~-~i—r~~.' é Hk‘xcosm) x’ i ,a, t ' Ol : 0,2660:'-l CM: (m QMA'QK) ‘ j“ / 2'1 .30 h ‘ 0 « aw Name x'Hi‘ ' Pag620f4 ! . Hour Test I Teaching Assistant 21 September 2000 3 2. (25) Compute the derivatives of a. f(x) 3x4 + x7“ — 2x—4 f/f)’: '- , + K.‘ - 4/ \3 .v . .r. K x I \J ‘L I - r‘“ "' .1, ‘ a? *" ‘ r, ‘ , t k § 1 J x t) k/l — ‘ ’7—~~§"z ‘ ”I , "K )- ‘ . 3/ / I ,‘ 2‘ - , ' / \- w L4 0 / M ; M : a J" .‘. / "g ”’2 0-4:; ‘ e‘! .2 t V 2! , " ”" , / , ”E/ (0 d. Fm = sin(4.\'3 + 2) I ’l l ‘3. , t Name yttrium? 6. , " Page3of4 , , Hour Test I Teaching Assistant ‘ ' 21 September 2000 3. (25) Let f(x) = x: — 6x + 7 3. Sketch the graph off. biti‘Find the equation of the line tangent to the graph offat the poinl‘fiffl», and sketch this line on your graph in part a. c. Calculate the area of the triangle formed by the x—axis, the y-axis, and the line tangent to the graph offal the point (2 ,f(2)). i a Name “.0 J 5 if "5' i 5 a” ;‘ " Page 4 Of 4 Hour Test I 21 September 2000 Teaching Assistant 4. (25) Water is being poured into a reservoir in the shape of a cone (point down) 6 feet tall with a radius of 4 feet. If the water level is rising at the rate of 0.5 feet per second, how fast is the water being poured in at the instant the depth is 2 feet?/ vii a ’ ' I 1, i 44‘ I .“L t - «rift; \" “f :7?er 3W\TA>L “a if“: H ‘ 27a 4 i L. c 4* 3: ~ I ”I: - JL‘ 1+ 435...? \ X F”: ' 32 . Ct ’74—— 5- 58C J+ é: * __ 77% (I. 1/ 9 Tr ...
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