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Bài tập CALCULUS 82
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Created by T. Madas
Question 273
(*****)
A curve C and a straight line L have respective equations
C : y = 4x x −
25 x 2
16
and
L : x + 2 y = 18 .
a) Show that L is a tangent to C , at some point to be found.
b) Verify the answer of part (a) by an alternative method.
c) Show further that L does not meet C again.
SPX-G , proof
Created by T. Madas
Created by T. Madas
Question 274
(*****)
The distinct points A , B and C lie on the curve with equation
xy = p 2 ,
where p is a positive constant.
Given that ABC is a right angle, show that the tangent to the curve at B , is
perpendicular to AC .
SP-C , proof
Created by T. Madas
Created by T. Madas
Question 275
(*****)
A quadratic curve has equation
(
)
f ( x ) ≡ x 2 + 6 x + 20 + k x 2 − 3 x − 12 ,
where k is a constant.
Given that the point P ( −2, p ) is the minimum point of the curve, determine the value
of each of the constants p and k .
MP1-T , p = 80 , k = 2
7
7
Created by T. Madas
