Bài tập CALCULUS 25

Created by T Madas Question 95 (***+) A curve has equation y = x −8 x , x∈» , x ≥ The curve meets the x axis at the origin and at the point P a) Determine the coordinates of P The point Q , where x = , lies on the curve b) Find an equation of the normal to curve at Q c) Show that the normal to the curve at Q does not meet the curve again SYN-N , P ( 64,0 ) , y = x − 16 Created by T Madas Created by T Madas Question 96 (***+) The diagram below shows a parabola and a straight line with respective equations y = − x + 11x − 24 and y =4 The points P and Q are the intersections between the parabola and the straight line y y = − x + 11x − 24 P Q y=4 x O Find the exact area of the shaded region, bounded by the curve, the coordinate axes and the straight line with equation y = C2C , area = 83 Created by T Madas Created by T Madas Question 97 (***+) Given that n is a positive integer greater than , show clearly that  n2 1− 2 dx = ( n − ) , x > x proof Question 98 (***+) ( ) The point P 4, lies on the curve C whose gradient function is given by dy x + 24 = , x ≠ dx x2 a) Determine an equation of the tangent to C at P b) Find an equation of C 24 +1 C1P , y = 21x − 82 , y = x − x Created by T Madas