- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập CALCULUS 02
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (924.32 KB, 3 trang )
Created by T. Madas
Question 3
(**)
y
y = ( 3 − x )( x + 1)
O
x
The figure above shows the curve with equation
y = ( 3 − x )( x + 1) , x ∈ » .
Find the exact area of the region, bounded by the curve and the x axis, shown shaded
in the figure above.
MP1-M , area = 32
3
Created by T. Madas
Created by T. Madas
Question 4
(**)
y = 2x2 −
6
x
3
+ 8 x3 , x ≠ 0 .
Find a fully simplified expression for
y dx .
C1A , 2 x3 + 3 x −2 + 2 x 4 + C
3
Question 5
(**)
f ( x ) = 2 x2 − 7 x + 1, x ∈ » .
Find the coordinates of the point on the curve with equation y = f ( x ) , whose gradient
is 5 .
( 3, −2 )
Created by T. Madas
Created by T. Madas
Question 6
(**)
y = x3 − 6 x 2 + 12 , x ∈ » .
Find the range of values of x for which y is decreasing.
C2E , 0 < x < 4
Question 7
(**)
y
y = ( x + 1)( x − 2 )( x − 4 )
x
O
The figure above shows the curve with equation
y = ( x + 1)( x − 2 )( x − 4 ) , x ∈ » .
a) Write the equation of the curve in the form y = x3 + ax 2 + bx + c , where a , b
and c are constants.
b) Find the exact area the shaded region.
C2D , y = x3 − 5 x 2 + 2 x + 8 , area = 16
3
Created by T. Madas
