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
1
y = 2+ , x ≠ 0.
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

8 y = 2x +1 .

d) Determine the coordinates of B .

(

C1F , x = 0, y = 2 , A − 1 ,0
2

Created by T. Madas

)


Created by T. Madas
Question 159

(***+)
y

O

A

B

x

R
8 − x3

y=
3x 2

The figure below shows part of the curve with equation

y=

8 − x3
3x 2

, 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, 0 ) , area = 4
3

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 − 1
, x>0.
x

a) Find an equation of the curve.
b) Determine the coordinates of P .
3

( )

C1C , f ( x ) = 8 x 2 − 2 x , P 1 , 0
4

Created by T. Madas