MATH 151, FALL 2005COMMON EXAM I I - VERSION ANAME (print):INSTRUCTOR:SECTION NUMBER:UIN:DIRECTIONS:1. The use of a calculator, laptop or computer is prohibited.2. In Part 1 (Problems 1-13), mark the correct choice on your ScanTron form No. 815-E using a No. 2 pencil. Foryour own records, also record your choices on your exam! ScanTrons will be collected from all examinees after 90minutes and will not be returned.3. In Part 2 (Problems 14-18), present your solutions in the space provided. Show all your work neatly and conciselyand clearly 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 it.4. Be sure to write your name, section number and version letter of the exam on the ScanTron form.THE AGGIE CODE OF HONOR“An Aggie does not lie, cheat or steal, or tolerate those who do”Signature:DO NOT WRITE BELOW!QuestionPoints Awarded Points1-13 5214 1415 816 817 818 101001PART I1. (4 pts) If f(x)=e4x−5e3x+3ex+ sin(x), then f0(0) =(a) 1(b) 0(c) −6(d) −7(e) −82. (4 pts) If F (x)=f(g(x)) where f (2) = 3 ,g(2) = 5 ,g0(2) = 4 ,f0(2) = −2 ,g0(3) = 7 and f0(5) = 11 , thenF0(2) =(a) 72(b) 44(c) 2(d) −8(e) −14Exam continues on next page23. (4 pts) Find limx→03x(1 + cos(x))sin(4x).(a)32(b)34(c) 0(d) −34(e) −324. (4 pts) Findddx(x cos(2x))(a) sin(2x) − 2x cos(2x)(b) sin(2x)+2xcos(2x)(c) cos(2x) − 2x sin(2x)(d) cos(2x)+2xsin(2x)(e) −2x sin(2x)Exam continues on next page35. (4 pts) Findddt(x2y)whenx=2 and y=3 giventhat dx/dt = −2anddy/dt =4.(a) 28(b) 16(c) −4(d) −8(e) −126. (4 pts) If f(x)=2x+1x+5, then the inverse function of f(x)is(a)x +52x+1(b)1+5xx+2(c)1+5xx−2(d)1 − 5xx − 2(e)2x +1x+5Exam continues on next page47. (4 pts) If h(t)=(t3−t2+t+1)3,then h0(−1) =(a) 216(b) 108(c) 72(d) 12(e) −68. (4 pts) Find limx→−∞ex−1.(a) ∞(b) e(c) 1(d)1e(e) 0Exam continues on next page59. (4 pts) If log4x +log4(x2)=6,then x=(a) 16(b) 8(c) 4(d) 2(e) 010. (4 pts) If f(x)=x5+2x+1 and g(x) denotes the inverse function of f (x), then g0(4) =(a) 4(b) 1(c)17(d)18(e)112Exam continues on next page6For problems 11-13, let the time t position of a particle be given by the vector function r(t)=ht3−4t2+2, 2t2−3ti .11. (4 pts) Find the position vector of the particle at time t =2.(a) h−6 , 2i(b) h−4 , 2i(c) h−2 , 4i(d) h0, 0i(e) h2, 4i12. (4 pts) Find the speed of the particle at time t =2.(a) h−2 , 6i(b) h−4 , 5i(c) h0 , 8i(d) 41(e)√4113. (4 pts) Find the acceleration of the particle at time t =2.(a) h1 , 2i(b) h4 , 4i(c) h4 , 2i(d) h−4 , 4i(e) h8 , 6iExam continues on next page7PART I I14. Find f0(x) for the following functions. Don0t simplify!(a) (7 pts) f(x)=cos(2x)sin(3x)+tan(4x)(b) (7 pts) f(x)=e√x2+3x+4Exam continues on next page815. (8 pts) Find the equation of the tangent line to the curve y5+3x2y3+x3+ 5 = 0 at the point (2, −1) .Exam continues on next page916. (8 pts) Starting with x1= −1 , use Newton’s method to find the approximation x2to the solution of the equationx5+ x3+1=0.Exam continues on next page1017. (8 pts) Find the quadratic approximation of4√x for x near 16.Exam continues on next page1118. (10 pts) A balloon is rising at a constant speed of 5 ft/sec. A boy is cycling along a straight road at a speed of 15ft/sec. When he passes under the balloon it is 45 ft above him. How fast is the distance between the boy and theballoon increasing 3 seconds later?End of
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