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Bài tập CALCULUS 25
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Created by T. Madas
Question 95
(***+)
A curve has equation
y = x −8 x , x∈» , x ≥ 0 .
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 = 4 , 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 2 + 11x − 24
and
y =4.
The points P and Q are the intersections between the parabola and the straight line.
y
y = − x 2 + 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 = 4 .
C2C , area = 83
6
Created by T. Madas
Created by T. Madas
Question 97
(***+)
Given that n is a positive integer greater than 2 , show clearly that
n2
1−
4
2
2
dx = ( n − 2 ) , x > 0 .
x
proof
Question 98
(***+)
( )
The point P 4, 1 lies on the curve C whose gradient function is given by
3
5
dy x 2 + 24
=
, x ≠ 0.
dx
x2
a) Determine an equation of the tangent to C at P .
b) Find an equation of C .
3
24
+1
C1P , 6 y = 21x − 82 , y = 2 x 2 −
3
x
Created by T. Madas
