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Bài tập CALCULUS 68
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Created by T. Madas
Question 234
(****)
The curve C has equation
4
y = 2 x3 − 3x + , x ≠ 0
x
The point P ( 2,12 ) lies on C .
a) Find the gradient at P .
b) Determine the coordinates of another point Q that lies on C , so that the
gradient at Q is the same gradient as P .
C1T , gradient = 20 , Q ( −2, −12 )
Created by T. Madas
Created by T. Madas
Question 235
(****)
y
( 0,1)
x + y =1
R
O
(1,0 )
x
The figure above shows the curve with equation
x + y = 1 , x ∈ » , 0 ≤ x ≤ 1.
The curve meets the coordinate axes at the points (1,0 ) and ( 0,1) .
The finite region R is bounded by the curve and the coordinate axes.
Show that the area of R is 1 .
6
SYN-I , proof
Created by T. Madas
Created by T. Madas
Question 236
(****) non calculator
The curve C has equation
y=
6 x2 + 1
, x>0
2 x
Show that an equation of the tangent to C at the point where x = 1 is
4
4 x − 16 y + 21 = 0 .
proof
Created by T. Madas
