Suppose that a rectangle is bounded by the x -axis and the graph of y = cos x . a. Write a function that represents the area A x of the rectangle for. 0 < x < π 2 b. Complete the table. a. Graph the function from part (a) on the viewing window: 0 , π 2 , π 6 by − 3 , 3 , 1 and approximate the values of x for which the area is 1 square unit Round to 2 decimal places. b. In calculus, we can show that the maximum value of the area of the rectangle will occur at values of x for which 2 cos x − 2 x sin x = 0 . Confirm this result by graphing y = 2 cos x − 2 x sin x and the function from part (a) on the same viewing window. What do you notice?
Suppose that a rectangle is bounded by the x -axis and the graph of y = cos x . a. Write a function that represents the area A x of the rectangle for. 0 < x < π 2 b. Complete the table. a. Graph the function from part (a) on the viewing window: 0 , π 2 , π 6 by − 3 , 3 , 1 and approximate the values of x for which the area is 1 square unit Round to 2 decimal places. b. In calculus, we can show that the maximum value of the area of the rectangle will occur at values of x for which 2 cos x − 2 x sin x = 0 . Confirm this result by graphing y = 2 cos x − 2 x sin x and the function from part (a) on the same viewing window. What do you notice?
Solution Summary: The author analyzes the function that represents the area of the rectangle for 0xpi 2.
Suppose that a rectangle is bounded by the x-axis and the graph of
y
=
cos
x
.
a. Write a function that represents the area
A
x
of the rectangle for.
0
<
x
<
π
2
b. Complete the table.
a. Graph the function from part (a) on the viewing window:
0
,
π
2
,
π
6
by
−
3
,
3
,
1
and approximate the values of
x
for which the area is
1
square unit Round to
2
decimal places.
b. In calculus, we can show that the maximum value of the area of the rectangle will occur at values of
x
for which
2
cos
x
−
2
x
sin
x
=
0
. Confirm this result by graphing
y
=
2
cos
x
−
2
x
sin
x
and the function from part (a) on the same viewing window. What do you notice?
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13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.
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SHOW ME ALL THE NEEDED STEPS
11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
please answer by showing all the dfalowing necessary step
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The sides of a cube of ice are melting at a rate of 1 inch per hour. When its volume is 64 cubic inches, at what rate is its volume changing?
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