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Bài tập CALCULUS 80
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Created by T. Madas
Question 267
(****+)
The gradient function of a curve satisfies the following relationship
( x + 1)
dy
+ 16 = 4 ( 2 x + y ) .
dx
The normal to the curve at the point P has equation x + 3 y = 6 .
Determine the coordinates of P .
SP-J , P ( 3,1)
Created by T. Madas
Created by T. Madas
Question 268
(****+)
A quartic curve C has equation
y = x3 ( x + 2 ) , x ∈ » .
a) Sketch the graph of C .
The sketch must contain the coordinates of any stationary points and the
coordinates of the points of intersection with the coordinate axes.
b) Show that there is only one point on C where the gradient is 10 .
MP1-R , proof
Created by T. Madas
Created by T. Madas
Question 269
(****+)
The function y = f ( x ) satisfies the following relationships
1
2
5 f ( x ) dx +
0
0
2
3 f ( x ) dx = 31
1
1 f ( x ) dx +
3
2
2 f ( x ) dx = 17 .
1
Determine the value of
2
f ( x ) dx .
0
SP-L , 9
Created by T. Madas
