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Bài tập CALCULUS 84
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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
