Tiêu đề Copy of T900 - MATHEMATICS N6 QP AUG 2016.pdf ✅

(16030186) -3- T900(E)(A5)T Copyright reserved Please turn over QUESTION 1 1.1 If z = ) cos (3 4 4 x  y determine y z   . (2) 1.2 Calculate 2 2 dx d y of the parametric equations 3 x  ln u and u y e 3  at the point where u = 1. (4) [6] QUESTION 2 Determine  y dx if: 2.1 y = 2 67  4x  2x (4) 2.2 y = x .arctan x 2 (3) 2.3 y = tan 7x.tan 7x 3 2 (5) 2.4 y = 2 .sin 2 cos4 x 3 x (4) 2.5 y = ax ln x (2) [18] QUESTION 3 Use partial fractions to calculate the following integrals: 3.1      ( 5 6) 1 2 2 2 x x x x x dx (5) 3.2      ( 3)( 6) 5 3 2 2 x x x x dx (7) [12]
(16030186) -4- T900(E)(A5)T Copyright reserved Please turn over QUESTION 4 4.1 Calculate the particular solution of : x y dx dy x x cos 1 cos sin         if y  2 when 5  x  (6) 4.2 Calculate the general solution of: 2 2 dx d y dx dy  5 + 6 y = x e 2 3  (6) [12] QUESTION 5 5.1 5.1.1 Sketch the graph of x y e 2  2 and show the representative strip/element that you will use to calculate the volume generated when the area bounded by the graph , x  0 y  0 and x  1 rotates about the y-axis. (2) 5.1.2 Calculate the volume described in QUESTION 5.1.1. (5) 5.2 5.2.1 Make a neat sketch of the graph 2 3cos x y  and show the representative strip/element that you will use to calculate the area bounded by the graph, the x-axis, the y-axis and the line x   . (2) 5.2.2 Calculate the area described in QUESTION 5.2.1. (3) 5.2.3 Calculate the distance of the centroid from the x-axis of the bounded area described in QUESTION 5.2.1. (5) 5.3 5.3.1 Calculate the points of intersection of the TWO curves 0 y  5x  and 5 2 y x  . Make a neat sketch of the TWO curves and show the area bounded by the curves. Show the representative strip/element that you will use to calculate the volume of the solid generated when the bounded area rotates about the x-axis. (3) 5.3.2 Calculate the magnitude of the volume described in QUESTION 5.3.1 by means of integration. (4) 5.3.3 Calculate the moment of inertia if the bounded area described in QUESTION 5.3.1 is rotated about the x-axis. (5) 5.3.4 Express the answer in QUESTION 5.3.3 in terms of the mass. (1)