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Bài tập CALCULUS 88
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Created by T. Madas
Question 291
(*****)
R
H
R
The figure above shows a hollow container consisting of a right circular cylinder of
radius R and of height H joined to a hemisphere of radius R .
The cylinder is open on one of the circular ends and the hemisphere is also open on its
circular base. The cylinder is joined to the hemisphere at their open ends so that the
resulting object is completely sealed.
Given that volume of the container is V , show the surface area of the container is
minimised when R = H , and hence show further that this minimum surface area is
3
45π V 2 .
SYN-W , proof
Created by T. Madas
Created by T. Madas
Question 292
(*****)
A curve C has equation
y=
2x + 3
, x∈» , x > 1 .
2
2x −1
Find the coordinates of the stationary point of C , further determining the nature of this
point.
You may not use the product rule, the quotient rule or logarithmic differentiation in
this question.
( )
SYN-U , max 5 , 4
2
Created by T. Madas
Created by T. Madas
Question 293
(*****)
The point P , whose y coordinate is 2 , lies on the curve with equation
y=
k + 8x x
, x∈» , x > 0 ,
12 x
where k is a non zero constant.
The tangent to the curve at P is parallel to the straight line with equation
6 x + y = 17 .
Determine the value of k .
SYN-T , k = 5
Created by T. Madas
