MATH 1190/12 SPRING SEMESTER 2005 OLD EXAM #3 - PageOut

MATH 1190/12SPRING SEMESTER 2005OLD EXAM #3PART IDIRECTIONS:a) Place your solution to each problem on a separate sheet of paper.b) You must show your work and give reasons for what you do. No credit will be given for unsupportedcorrect answers.c) No credit will be given for correct answers that result from erroneous arguments.d) You are expected to abide by the University's rules regarding academic honesty.1. Suppose that is a continuous function and , , , for, for , for , for or , and lim lim . Sketch the graph of .2. Find the most general antiderivative of each of the following functions.a) b) c) 3. Use l'Hospital's rule to find each of the following limits or explain why it does not exist. a) lim b) lim 4. The graph of the first derivative of a function is given below. Use it to answer questions (a) – (d). (a) On what interval(s) is increasing? __________________________________

7. Find the interval on which the graph of ln is concave upward.a) b) c) d) e) f) None of the above.8. Find the value of the limit lim .cos a)b) c) d) e) f) None of the above.9. Find the value of the limit lim . a) b) c) ln d) e) f) None of the above.0. Farmer Brown wants to fence in a rectangular plot in a large field, using a rock wall which is already there asthe north boundary. The fencing for the east and west sides of the plot will cost $ /yard, but she needs touse special fencing which will cost $ /yard on the south side of the plot. If the area of the plot is to be square yards, find the dimensions for the plot which will minimize the cost of the fencing. Dimensions beloware listed east by south.a) by yards b) by yardsc) by yards d) by yardse) by 15 yards f) None of the above.1. Find the most general antiderivative of sec sin. a)sec sin b) tan sinc) tancos d) tancose) tan sinf) None of the above. 2. If , , and , find .a) b) c) d) e) f) None of the above.ANSWERSPART I1.

..4.a) ln b) c)a) b) a) b) c) d) , 5.a) , and b) Length in, Width in 6. PART II1) C, 2) B, 3) E, 4) B, 5) A, 6) B, 7) A, 8) D, 9) E, 10) C, 11) D, 12) E