Transcription of MATH 151 FALL SEMESTER 2011 COMMON …
1 MATH 151, fall SEMESTER 2011 COMMON EXAMINATION I-VERSION BName (print):Instructor s name:Signature:Section No:Part 1 Multiple Choice(12 questions,4 points each,No Calculators)Write your name, section number, and version letter (B) of the exam on the ScanTron your responses on the ScanTron form and on the exam 4, 2 andw 6i 2j. Compute12v ball whose weight is50 Newtons hangs fromtwo wires, one at angle23 from horizontal,and the other at angle37 from the tension in the first wire, andT2be the tension in the second set of equations can be used to solveforT1andT2?a.|T1|cos 23 |T2|cos 37 0and |T1|sin 23 |T2|sin 37 50b. |T1|cos 23 |T1|cos 37 0and|T2|sin 23 |T2|sin 37 50c.|T1|cos 23 |T2|cos 37 50and |T1|sin 23 |T2|sin 37 0d. |T1|cos 23 |T2|cos 37 50and |T1|sin 23 |T2|sin 37 0e. |T1|cos 23 |T2|cos 37 0and|T1|sin 23 |T2|sin 37 the angle between the vectorsv 1, 3andw 3, the scalar projection (component) and vector projection ofv 5i 12jontow 4i projection 1613vector projection 64169i projection 1613vector projection 80169i projection 165vector projection 6425i projection 165vector projection 6425i projection 165vector projection 6425i the Cartesian equation for the graph of the parametric curvex 1 tandy t2 x2 x2 x2 x2 3x x2 3x a vector equation for the line which contains the point 3, 4 and is parallel to 1, 2.
2 T 4 2t, 3 t t 3 t, 4 2t t 3 t, 4 2t t 1 3t, 2 4t t 1 3t, 2 4t x x2 5x 6 x 2 2. Which of the following is true? 2 f x andlimx 2 f x 2 f x andlimx 2 f x 2 f x andlimx 2 f x 2 f x andlimx 2 f x of 31t 13t 1/9d. 1 not interval contains the unique real solution of the equation2x3 x 1 0?a. 2, 1 b. 1, 0 c. 0, 1 d. 1, 2 e. 2, 3 of the following is a horizontal asymptote off x 2x2 3 x 3 x 3 ? of the 2 2x2 4x x 4 a. b. 3x2 2xx 2a. 32d. 1e. 3 Part 2 Work Out Problems(5 Calculators)Solve each problem in the space provided. Show all your work neatly and concisely, andindicate your final answer clearly. You will be graded, not merely on the final answer, but also onthe quality and correctness of the work leading up to (10 points) An object is moving in thexy-plane and its position vector aftertseconds isr t t 2,t2 3t . the position vector of the object at timet the object pass through the point 1, 0 ?
3 If yes, when? If no, why not? the object pass through the point 2, 8 ? If yes, when? If no, why not?14.(14 points) Sketch the graph of the functiong x 1 xifx 13ifx 1|x|if 1 x 2x2 3ifx 2 Then determine each of the following-3-2-1123-2-112345limx 1 g x limx 1 g x g 1 limx 2 g x limx 2 g x g 2 List all value(s) of x whereg x is NOT differentiable:415.(9 points) Compute each of the following or prove the limit does not 3 |x 3|x2 3x 3 |x 3|x2 3x 3|x 3|x2 3x 16.(9 points) Considerf x x2 x 6x 3ifx 3pifx 3f x or explain why it does not the value(s) ofpthat makef x continuous atx 3or explain why no (10 points) Consider the functionf x x , the derivative off x , using the limit definition of the the slope of the tangent line to the curvey f x atx (print):Section No:QuestionPoints/Max1-12/4813/1014/1415 / 916/ 917/10 Total/1006
