MA123 Exam 120 September 2006Problem Answer123456789101112131415a b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d ea b c d eInstructions. 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) b e foreyou begin. You may use the following formula for the derivative of a quadraticfunction. Ifp(x) = Ax2+ Bx + Cthenp0(x) = 2Ax + B11. If h(x) =√x2+ 1 and g(x) = 2x − 1 then h(g(x)) =(a) 4x(b)√4x2− 4x + 2(c) 2√x2+ 1 − 1(d)√4x2− 4x + 2(e) 2x2− 12. If u(t) = t + 7 then u(v(x)) = x if v(x) =(a) x + 7(b) 1(c) x − 7(d) 0(e) x3. The inequality x2+ x − 2 > 0 is equivalent to(a) x < −2 or x > 1(b) −2 < x and x < 1(c) x = −2 or x = 1(d) x < −√2 or x > 1(e) x = −√2 and x = 124. Suppose F (x) =√x2− 2x − 3 . What is the largest value of A such thatF (x) is defined on the interval [−5, A] ?(a) −4(b) −3(c) −2(d) −1(e) 05. An equation of a line through the points (3, 5) and (8, 7) in the (s, t) planeis(a) s = 6 + 5(t − 5)(b) t = 6 + 5(s − 5)(c) 2t = 6 + 5(s − 5)(d) 2s = 6 + 5(t − 5)(e) s = 5 + 6(t − 5)6. If f(t) = 1/t thenf(t + h) −f(t)h=(a) 1/(h2)(b) 1/(t(t + h))(c) (−1)/(t(t + h))(d) 1/(t(t − h))(e) −1/(t(t − h))37. A train travels from A to B to C. The distance from A to B is 30 milesand the distance from B to C is 80 miles. The train leaves A at 10:00 AMand arrives at C at 3:00 PM. The average speed from A to B was 30 milesper hour. What was the average speed from B to C in miles per hour?(a) 20(b) 25(c) 30(d) 35(e) 408. If g(x) = |x − 7| what is the average rate of change of g(x) with respectto x as x changes from −3 to 3?(a) −2(b) −1(c) 0(d) 1(e) 29. If g(s) = 3s2+ s −2 what is the value of g(s) when the instantaneous rateof change of g(s) with respect to s equals 1?(a) −2(b) −1(c) 0(d) 1(e) 2410. Suppose g(s) = s2+ 1. Find a point of the graph of t = g(s) such thatthe tangent line to the graph is parallel to the line with equation t = s.(a) (0, 1)(b)12,54(c) (1, 2)(d)32,134(e) (2, 5)11. Suppose f(t) = t3+ 1 . Find a value A greater than 0 such that theaverage rate of change of f (t) from 0 to A equals 2.(a) 1(b)√2(c)√3(d) 2(e)√512. Supposef(t) =(−t)2if t < 1t3if t ≥ 1Find the limitlimt→1f(t)(a) −2(b) −1(c) 1(d) 2(e) The limit does not exist513. Supposef(t) =t if t ≤ 3A +t2if t > 3Find a value of A such that the function f(t) is continuous for all t.(a) 1/2(b) 1(c) 3/2(d) 2(e) 5/214. Find the limitlimt→0+√t3√t(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 equalsa fixed cost of $1000 plus $3 times the quantity produced. So total costin dollars isC(q) = 1000 + 3qThe average c ost 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 0 from the right. In other words findlimq→0+A(q)(a) 0(b) 3(c) 1000(d) 1003(e) The limit does not
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