- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập CALCULUS 16
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (924.36 KB, 3 trang )
Created by T. Madas
Question 64
(***)
y = x − 2 x4 , x ∈ » .
a) Find the coordinates of the stationary point of y and determine its nature.
b) Show clearly that y has no points of inflection.
( )
C2N , max 1 , 3
2 8
Question 65
(***)
dy
1
= 4+ 2 , x ≠ 0.
dx
x
Given that y = 5 when x = 1 , express y in terms of x .
C1Q , y = 4 x −
Created by T. Madas
1
+2
x
Created by T. Madas
Question 66
(***)
y
L
y= x
P
R
O
x
4
The figure above shows the graph of the curve C with equation
y= x , x≥0.
The point P lies on C where x = 4 .
The straight line L is the tangent to C at P .
a) Find an equation of L .
The finite region R , shown shaded in the figure, is bounded by C , L and the x axis.
b) Find the exact area of R .
MP1-D , y = 1 x + 1 , 8
3
4
Created by T. Madas
Created by T. Madas
Question 67
(***)
The curve C has equation
f ( x) =
( 2 x − 3)( x + 2 ) ,
x
3
1
x >0.
a) Express f ( x ) in the form Ax 2 + Bx 2 + Cx
− 12
, where A , B and C are
constants to be found.
b) Show that the tangent to C at the point where x = 1 is parallel to the line with
equation
2 y = 13 x + 2 .
A = 2 , B = 1 , C = −6
Created by T. Madas
