Calculus for Business and Social Sciences - Final Exam Review | MATH 241, Exams of Mathematics

Download Calculus for Business and Social Sciences - Final Exam Review | MATH 241 and more Exams Mathematics in PDF only on Docsity! MATH 241, REVIEW FOR FINAL EXAM 0.1. Short Answer. (1) The slope of the secant line to y = x2 from x = −1 to x = 2 is (a) -2 (b) 4 (c) 1 (d) 0 (e) undefined (2) limx→3 x 2−2x−3 x−3 is equal to (a) 0 (b) 2 (c) -2 (d) 4 (e) undefined (3) limx→∞ 3x+5x 3−7 x3+2x2+1 is equal to (a) 3 (b) 5 (c) 3 2 (d) 5 2 (e) undefined (4) If f(1) = 2, g(1) = −1, f ′(1) = 0 and g′(1) = 5 then the derivative of fg when x = 1 is equal to (a) -10 (b) 5 (c) 2 (d) -1 (e) 0 (5) Give a complete statement of the chain rule. (6) A singular point is a place where (choose the best answer): (a) A function is at its maximum. (b) The second derivative is zero. (c) The derivative is zero. (d) The limit goes to infinity. (e) The derivative is undefined. (7) The stationary point of the function 4x− x2 is: (a) (0,0) (b) (4, 0) (c) (1,3) (d) (2,4) (e) (-1, -5) (8) The maximum value attained by the function f(x) = x3 + 3x2 + 3x + 5 over the interval from −2 to 3 is: (a) 32 (b) 16 (c) 4 (d) 3 (e) none of the above. (9) The derivative of ln x−1x+1 is equal to: (a) x−1x+1 (b) x+1 x−1 (c) 1 x−1 − 1 x+1 (d) −2 (x−1)2 (e) undefined (10) If x2 + y2 = 25, then dydx at the point (5, 0) is (a) 3 (b) 5 (c) -5 (d) −4 3 (e) undefined (11) The greatest value taken by the function e−x 2 is (a) 0 (b) e (c) e2 (d) 1 (e) there is no global maximum 1