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Bài tập CALCULUS 86
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Created by T. Madas
Question 285
(*****)
The point P lies on the curve with equation y = x 2 , so that its distance from the point
A (10, 2 ) is least.
Determine the coordinates of P and the distance AP .
P ( 2, 4 ) , d min = 2 17
Created by T. Madas
Created by T. Madas
Question 286
(*****)
The curve with equation y = x 2 , x ∈ » , is translated parallel to the x axis, so that R
denotes the area of the finite region bounded by the coordinated axes, the curve and the
straight line with equation x = 3 .
Determine the least value of R .
MP1-S , 9
4
Created by T. Madas
Created by T. Madas
Question 287
(*****)
y
y = A− xp
−2
x
2
O
y = B − xq
The figure above shows the curves with equations
y = A − x p and y = B − x q ,
where A and B are positive constants with A > B , and p and q are positive integers
with p + q = 8 .
Both curves meet the x axis at the points ( −2,0 ) and ( 2,0 ) .
Find the exact value of the area bounded between the two curves.
SP-Q , area =
Created by T. Madas
4384
21
