Bài tập CALCULUS 24

Created by T Madas Question 91 (***+) y y = ( x − 2) A y = x − x + 16 B O x The figure above shows the graph of the curves with equations y = ( x − 2) and y = x − x + 16 The curves meet each other at the points A and B a) Determine the coordinates of A and B b) Find the exact area of the finite region bounded by the two curves, shown shaded in the above figure ( ) MP1-E , A ( 0,16 ) B ,9 , 343 24 Created by T Madas Created by T Madas Question 92 (***+) 3x2 − ) ( f ( x) = x2 , x ≠ Show clearly that  f ( x ) dx = 11 proof Question 93 (***+) The curve C has equation y= 3−8 x , x>0 x Show clearly that d2y dx = ( 1− x x ) proof Created by T Madas Created by T Madas Question 94 (***+) r h A pencil holder is in the shape of a right circular cylinder, which is open at one of its circular ends The cylinder has radius r cm and height h cm and the total surface area of the cylinder, including its base, is 360 cm a) Show that the volume, V cm3 , of the cylinder is given by V = 180r − π r b) Determine by differentiation the value of r for which V has a stationary value c) Show that the value of r found in part (b) gives the maximum value for V d) Calculate, to the nearest cm3 , the maximum volume of the pencil holder r= Created by T Madas 120 π ≈ 6.18 , Vmax ≈ 742