Bài tập CALCULUS 09

Created by T Madas Question 34 (**+) y y = x+3 y = + x − x2 R B A x O The figure above shows the graph of the curve C with equation y = + x − x2 , and the straight line L with equation y = x+3 The curve meets the straight line at the points A and B The finite region R , shown shaded in the figure, is bounded by the curve C , the straight line L and the coordinate axes Show that the area of R is 13.5 square units SYN-A , proof Created by T Madas Created by T Madas Question 35 (**+) A curve has equation y = x3 − 10 x + , x ∈ » The point P ( 2, −10 ) lies on the curve The straight lines l1 and l2 are the tangent and the normal to the curve at P , respectively a) Find an equation for l1 and an equation for l2 l1 crosses the x axis at A and l2 crosses the y axis at B b) Find the area of the triangle OAB where O is the origin C1C , y = x − 14 , y + x + 18 = , area = 31.5 Created by T Madas Created by T Madas Question 36 (**+) By showing clear workings, find the value of  x− dx x C2I , 80 Question 37 (**+) Find the value of the constant k , k > , given that  k x − dx = 28 k=9 Created by T Madas