In the following exercises, evaluate the triple integrals over the bounded legion E = { ( x , y , z ) | a ≤ x ≤ b , h 1 ( x ) ≤ y ≤ h 2 ( x ) , e ≤ z ≤ f } 193. ∭ E ( sin x + sin y ) d V , where E = { ( x , y , z ) | 0 ≤ 1 x ≤ π 2 , − cos x ≤ y cos x , − 1 ≤ z ≤ 1 }
In the following exercises, evaluate the triple integrals over the bounded legion E = { ( x , y , z ) | a ≤ x ≤ b , h 1 ( x ) ≤ y ≤ h 2 ( x ) , e ≤ z ≤ f } 193. ∭ E ( sin x + sin y ) d V , where E = { ( x , y , z ) | 0 ≤ 1 x ≤ π 2 , − cos x ≤ y cos x , − 1 ≤ z ≤ 1 }
In the following exercises, evaluate the triple integrals over the bounded legion
E
=
{
(
x
,
y
,
z
)
|
a
≤
x
≤
b
,
h
1
(
x
)
≤
y
≤
h
2
(
x
)
,
e
≤
z
≤
f
}
193.
∭
E
(
sin
x
+
sin
y
)
d
V
,
where
E
=
{
(
x
,
y
,
z
)
|
0
≤
1
x
≤
π
2
,
−
cos
x
≤
y
cos
x
,
−
1
≤
z
≤
1
}
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Given: Circle J
2
What is the value of y?
A. 38
C.
68
B. 50
D. 92
please find the answers for the yellows boxes using the information and the picture below
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
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