- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập CALCULUS 15
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (627.91 KB, 3 trang )
Created by T. Madas
Question 60
(***)
y
y = 2 x ( x − 1)( x − 3)
O
x
A
B
The figure above shows part of the curve with equation
y = 2 x ( x − 1)( x − 3) , x ∈ » .
The curve meets the x axis at the origin and at the points A and B .
Determine the exact area of the finite region bounded by the curve and the x axis,
shown shaded in the figure above.
C2B , area = 37
6
Created by T. Madas
Created by T. Madas
Question 61
(***)
h
x
4x
The figure above shows a box in the shape of a cuboid with a rectangular base x cm
by 4x cm and no top. The height of the box is h cm .
It is given that the surface area of the box is 1728 cm2 .
a) Show clearly that
864 − 2 x 2
.
h=
5x
b) Use part (a) to show that the volume of the box , V cm3 , is given by
(
)
V = 8 432 x − x3 .
5
c) Find the value of x for which V is stationary.
d) Find the maximum value for V , justifying the fact that it is the maximum.
x = 12 , Vmax = 5529.6
Created by T. Madas
Created by T. Madas
Question 62
(***)
The curve C and the line L have equations
C : y = 16 x +
32
− 35 and L : 2 y + x = 14 .
x
Show that L is a normal to C at the point where x = 4 .
proof
Question 63
(***)
The curve C has equation
y = ax 2 − 4 x +
8
, x >0,
x
where a is a non zero constant.
Given that
dy
= 0 at the point on C where x = 4 , find the value of a .
dx
C1H , a = 3
16
Created by T. Madas
