- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập CALCULUS 72
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (628.99 KB, 3 trang )
Created by T. Madas
Question 247
(****+)
12x
H
G
D
C
y
E
F
x
A
B
10x
The figure above shows the design of a baking tray with a horizontal rectangular base
ABCD , measuring 10x cm by y cm .
The faces ABFE and DCGH are isosceles trapeziums, parallel to each other.
The lengths of the edges EF and HG are 12x cm .
The faces ADHE and BCGF are identical rectangles.
The height of the tray is x cm .
The capacity of the tray is 1980 cm3 .
a) Show that the surface area, A cm 2 , of the tray is given by
A = 22 x 2 +
360
5+ 2 .
x
(
)
b) Determine the value of x for which A is stationary, showing that this value of
x minimizes the value for A .
c) Calculate the minimum surface area of the tray.
SYN-K , x ≈ 3.744 , Amin ≈ 925
[solution overleaf]
Created by T. Madas
Created by T. Madas
Created by T. Madas
Created by T. Madas
Question 248
(****+)
5
y
y = x 2 − 8x
A
O
x
R
L1
L2
The figure above shows the graph of the curve C with equation
5
y = x 2 − 8x , x ≥ 0 .
The curve meets the x axis at the origin O and at the point A .
The tangent to C at O is denoted by L1 and the tangent to C at A is denoted by L2 .
The finite region R , shown shaded in the figure above, is bounded by C , L1 and L2 .
Determine the area of R .
384 ≈ 11.0
35
Created by T. Madas
