Tải bản đầy đủ (.pdf) (3 trang)

Bài tập CALCULUS 84

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (493.27 KB, 3 trang )

Created by T. Madas
Question 279

(*****)

y

O

C

A

D

B

x

The figure above shows a cubic curve whose coefficient of x3 is 1 .
The curve crosses the x axis at A ( a,0 ) and touches the x axis at B ( b,0 ) , where a
and b are positive constants.
The point C is a local maximum of the curve.
The point D lies on the x axis so that CD is parallel to the y axis.
Show, with a detailed method, that
AB = 3 AD .

SYN-O , proof

Created by T. Madas



Created by T. Madas
Question 280

(*****)

A solid right circular cylinder of fixed volume has radius r and height h .
Show clearly that when the surface area of the cylinder is minimum h : r = 2 :1 .

proof

Created by T. Madas


Created by T. Madas
Question 281

(*****)

y
y = A − x 2a

x

2
O

y = B − x 2b

The figure above shows the curves with equations

y = A − x 2 a and y = B − x 2b , x ≥ 0 ,

where A and B are positive constants with A > B , and a and b are positive integers
with a + b = 4 .
Both curves meet the x axis at the point ( 2,0 ) .
Find the exact value of x for which both curves have the same gradient.
− 14

SP-F , x = 3

Created by T. Madas



Tài liệu bạn tìm kiếm đã sẵn sàng tải về

Tải bản đầy đủ ngay
×