- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập CALCULUS 08
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (879.15 KB, 3 trang )
Created by T. Madas
Question 29
(**+)
y
y = 4 − x − x2
B
A
y=2
x
O
The figure above shows a quadratic curve and a straight line with respective equations
y = 4 − x − x 2 and
y =2.
The points A and B are the points of intersection between the quadratic curve and the
straight line.
a) Find the coordinates of A and B .
b) Determine the exact area of the finite region bounded by the quadratic curve
and the straight line, shown shaded in the above figure.
MP1-A , A ( −2, 2 ) , B (1, 2 ) , area = 9
2
Created by T. Madas
Created by T. Madas
Question 30
(**+)
f ( x ) ≡ x3 − 5 x 2 + 3x + 1 , x ∈ » .
Find the range of values of x , for which f ( x ) is decreasing.
C2I , 1 < x < 3
3
Question 31
(**+)
y=3x+
Show clearly that the value of
d2y
dx 2
27
, x∈», x > 0 .
x
where x = 27 , is
4
.
2187
proof
Created by T. Madas
Created by T. Madas
Question 32
(**+)
The curve C has equation
3
y = 3x 2 − 6 x 2 + x − 5 , x ≥ 0 .
Find an equation of the normal to C at the point where x = 4 .
7y + x +3 = 0
Question 33
(**+)
f ( x ) ≡ x + 10 +
25
, x ≠ 0.
x
Find the coordinates of the two stationary points of f ( x ) and use f ′′ ( x ) to determine
their nature.
C2K , min ( 5, 20 ) , max ( −5,0 )
Created by T. Madas
