Bài tập CALCULUS 43

Created by T Madas Question 158 (***+) y C L B A x O The figure above shows a sketch of the curve C with equation y = 2+ , x ≠ x The dotted line represents an asymptote to C and the point A is the point where C crosses the x axis a) State the equations of the two asymptotes to the C b) Find the coordinates of A The straight line L is the normal to C at A , and B is the point where L meets C again c) Show that an equation for L is y = 2x +1 d) Determine the coordinates of B ( C1F , x = 0, y = , A − ,0 Created by T Madas ) Created by T Madas Question 159 (***+) y O A B x R − x3 y= 3x The figure below shows part of the curve with equation y= − x3 3x , x>0 The curve meets the x axis at the point A and B has coordinates ( 4,0 ) a) Find the coordinates of A b) Determine the exact area of the finite region R , bounded by the curve , the vertical line through B and the x axis C ( 4, ) , area = Created by T Madas Created by T Madas Question 160 (***+) y y = f ( x) O x P The figure above shows a curve with equation y = f ( x ) which meets the x axis at the origin O and at the point P The gradient function of the curve is given by f ′( x) = 12 x − , x>0 x a) Find an equation of the curve b) Determine the coordinates of P ( ) C1C , f ( x ) = x − x , P , Created by T Madas