The ratio R 1 ( n ) of the area of the region bounded by the graphs of y = a x n , y = a b n and x = 0 to the area of the circumscribed rectangle using the graph as shown below.
The ratio R 1 ( n ) of the area of the region bounded by the graphs of y = a x n , y = a b n and x = 0 to the area of the circumscribed rectangle using the graph as shown below.
To calculate: The ratio R1(n) of the area of the region bounded by the graphs of y=axn, y=abn and x=0 to the area of the circumscribed rectangle using the graph as shown below.
(b)
To determine
To calculate: The limit limn→∞R1(n) and compare it with the area of circumscribed rectangle using the graph as shown in the figure below:
(c)
To determine
To calculate: The volume of the solid of revolution formed by revolving the region about the y-axis and find the ratio R2(n) of this volume to the volume of circumscribed right circular cylinder using the graph as shown in the figure below:
(d)
To determine
To calculate: The limit limn→∞R2(n) and compare it with the volume of circumscribed cylinder using the graph as shown in the figure below:
(e)
To determine
A conjecture about the shape of the graph of y=axn, 0≤x≤b as n→∞ from the result of part (b) and part (d).
Decide whether each limit exists. If a limit exists, estimate its
value.
11. (a) lim f(x)
x-3
f(x) ↑
4
3-
2+
(b) lim f(x)
x―0
-2
0
X
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Determine whether the lines
L₁ (t) = (-2,3, −1)t + (0,2,-3) and
L2 p(s) = (2, −3, 1)s + (-10, 17, -8)
intersect. If they do, find the point of intersection.
Convert the line given by the parametric equations y(t)
Enter the symmetric equations in alphabetic order.
(x(t)
= -4+6t
= 3-t
(z(t)
=
5-7t
to symmetric equations.