Transcription of MATH 151, FALL 2009 COMMON EXAM II - …
1 math 151, fall 2009 COMMON EXAM II - VERSION BLAST NAME, First name (print):INSTRUCTOR:SECTION NUMBER:UIN:SEAT NUMBER:DIRECTIONS:1. The use of a calculator, laptop or computer is In Part 1 (Problems 1-11), mark the correct choice on your ScanTron using a No. 2 your own records,also record your choices on your exam!3. In Part 2 (Problems 12-17), present your solutions in the space all your workneatly and conciselyandclearly indicate your final answer. You will be graded not merely on the final answer, but also on the qualityand correctness of the work leading up to Be sure towrite your name, section number and version letter of the exam on the ScanTron AGGIE CODE OF HONOR An Aggie does not lie, cheat or steal, or tolerate those who do.
2 Signature:DO NOT WRITE BELOW!QuestionPoints AwardedPoints1-1144121513101410155166171 01001 PART I: Multiple Choice1. (4 pts) limx 2sin(x 2)x2+ 2x 8=(a) 1(b)16(c)14(d)15(e) The limit does not (4 pts) Findf (1) forf(x) =e x2.(a)4e(b)6e(c)1e(d)2e(e) 6e3. (4 pts) Find the tangent vector of unit length forr(t) =h4 cost,2 sintiatt= 3.(a) 2 7, 37 (b) 3 7, 27 (c) 2 3 13,1 13 (d) 2 7, 37 (e) 1 13,2 3 13, 24. (4 pts) Ifh(x) =xf(x3),f(2) = 4,f(8) = 3 andf (8) = 1, findh (2).(a)h (2) = 12(b)h (2) = 21(c)h (2) = 24(d)h (2) = 2(e)h (2) = 85. (4 pts) FindQ(x), the quadratic approximation, forf(x) = cos(2x) atx= 0.(a)Q(x) =x2(b)Q(x) = 1 +x 2x2(c)Q(x) = 1(d)Q(x) = 1 2x2(e)Q(x) = 1 +x+ 2x26.
3 (4 pts) limx 3 e1x+3=(a) 1(b) (c) (d) 0(e)e37. (4 pts) Given the curve parameterized byx=t2+ 5,y= t, what is the slope of the tangent line at the point(21,2)?(a)m= 82 21(b)m=132(c)m=182 21(d)m=12(e)m= 328. (4 pts) An object is moving according to the equation of motions(t) = cost+14t2. Find the time(s) when theacceleration is zero for 0 t 2 .(a)t= 3andt=2 3(b)t= 3andt=5 3(c)t= 6andt=5 6(d)t= 6andt=11 6(e)t=2 3andt=4 39. (4 pts) What is the slope of the tangent line to the curvex3+y3= 6xyat the point (3,3)?(a) 97(b) 1(c)97(d) 5(e) 1410. (4 pts) A particle moves according to the equation of motions(t) =t2 2t+ 3 wheres(t) is measured in feet andtis measured in seconds.
4 Find the total distance traveled in the first 3 seconds.(a) 2 feet(b) 4 feet(c) 9 feet(d) 11 feet(e) 5 feet11. (4 pts) Find all point(s) on the curvex=t2 2t+ 4,y=t3 3t2where the tangent line is vertical.(a) (4,0) and (4, 4)(b) (3, 2)(c) (1,0)(d) (0,0) and (2,2)(e) (4,4)5 PART II WORK OUTD irections: Present your solutions in the space all your workneatly and concisely andBox yourfinal answer. You will be graded not merely on the final answer, but also on the quality and correctness of the workleading up to (15 points total) Find the derivative of:(i) (5 pts)f(x) =xcos4(x3)(ii) (5 pts)g(t) =3 6t t2(iii) (5 pts)h(x) =esec x613. (10 pts) The altitude of a triangle is decreasing at a rateof12cm per minute while the area is increasing at a rateof 2 cm2/min.
5 How fast is the base of the triangle changing when the altitude is 6 cm and the area is 30 cm2?714. (10 pts) Finddydxfor sin(5y+ 7x) = 4x2+ (5 pts) Iff(x) =e3x+ 6x+ 1, findg (2) whereg=f 1, the inverse (6 pts) Given thatf(x) =3x+ 15 x, findf 1(x)Exam continues on next page917. (a) (5 pts) Find the linear approximation forf(x) = xatx= 4.(b) (5 pts) Approximate
