MA123 Exam 1September 19 2007Instructions. Circle your answer in ink on the page containing the problemand on the cover sheet. After the exam b egins , you may not ask a questionabout the exam. Be sure you have all pages (containing 15 problems) beforeyou begin. You may use the following formula for the derivative of a quadraticfunction. Ifp(x) = Ax2+ Bx + Cthenp0(x) = 2Ax + B11. If h(x) =1x2+1and g(3) = −1 then h(g(3)) =(a) 1/10(b) 1/5(c) 1/2(d) 1/3(e) undefined2. If u(t) =1t+1then u(v(x)) = x if v(x) =(a) 1/(x − 1)(b) 1/(x + 1)(c) (1/x) + 1(d) (1/x) − 1(e) x3. The inequality |x − 1| > 2 is equivalent to(a) x < 2 or x > 1(b) 2 < x and x < 1(c) x > 3 or x < −1(d) x > 3 or x < 1(e) x > 2 and x > 124. Suppose F (x) = 1/(x2− 5) . What is the largest value of A such thatF (x) is defined on the interval [−10, A) ?(a) −√5(b) −1(c) 0(d) 1(e)√55. The line defined by the equation y = 2+A(x−1) passes through the point(5, 3). The slope of the line is(a) 0(b) 1/4(c) 1/2(d) 2(e) 46. If f(t) = 3t2+ 4 thenf(1 + h) − f(1)h=(a) 4 + 3h(b) 3 + 4h(c) 6 + 3h(d) 8 + 3h(e) 8 + 4h37. A train travels from A to B to C. The distance from A to B is 10 milesand the distance from B to C is 40 miles. The average speed from A toB was 20 miles per hour and the average speed from B to C was 40 milesper hour. What was the average speed from A to C in miles per hour?(a) 180/5(b) 90/3(c) 100/3(d) 180/3(e) 100/58. If g(x) = (x − 1)2what is the average rate of change of g(x) with respectto x as x changes from −3 to 3?(a) −4(b) −2(c) 0(d) 2(e) 49. If g(s) = 3s2+ 2s − 2 what is the value of s for which the instantaneousrate of change of g(s) with respect to s equals 8?(a) −2(b) −1(c) 0(d) 1(e) 2410. Suppose g(s) = s2+ 4s + 1. Find a point of the graph of t = g(s) suchthat the tangent line to the graph is parallel to the s axis.(a) (2, 9)(b) (−1, −2)(c) (−2, −3)(d) (−4, 8)(e) (−4, 1)11. A train travels from city A to city B. Th e cities are 600 miles apart. Thedistance from city A at t hours after it leaves A is given byd(t) = 50t + t2What is the average speed of the train in miles per hour during the tripfrom A to B? Hint: First find how long it takes for the train to get fromA to B.(a) 50(b) 55(c) 60(d) 65(e) 7012. Supposef(t) =−t if t < 1t2if t ≥ 1Find the limitlimt→1f(t)(a) −1(b) 1(c) 0(d) 2(e) The limit does not exist513. Supposef(t) =Bt if t ≤ 35 if t > 3Find a value of B such that the function f (t) is continuous for all t.(a) 3/5(b) 4/5(c) 5/3(d) 5/4(e) 5/214. Find the limitlimt→∞31 + t2(a) 0(b) 1(c) 2(d) 3(e) The limit does not exist15. Suppose the total cost, C(q), of producing a quantity q of a product isgiven by the equationC(q ) = 5000 + 5qThe average cost per unit quantity, A(q), equals the total cost, C(q),divided by the quantity produced, q. Find the limiting value of the averagecost per unit as q tends to ∞. In other words findlimq→∞A(q)(a) 5(b) 6(c) 5000(d) 5006(e) The limit does not
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