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?
2. Graph the function f(x)=e* −1. Label three points on the graph (one should be the intercept) with
corresponding ordered pairs (round to one decimal place) and label the asymptote with its equation. Write the
domain and range of the function in interval notation. Make your graph big enough to see all important features.
You may show the final graph only.
ansewer both questions in a very detailed manner . thanks!
Question
Considering the definition of f(x) below, find lim f(x).
Select the correct answer below:
-56
-44
○ -35
○ The limit does not exist.
x+6
-2x² + 3x
2
if x-4
f(x) =
-x2
-x-2
if -4x6
-x²+1
if x > 6
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