Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. Let R be the unit disk centered at (0,0). Then ∬ R ( x 2 + y 2 ) d A = ∫ 0 2 π ∫ 0 1 r 2 d r d θ . b. The average distance between the points of the hemisphere z = 4 − x 2 − y 2 and the origin is 2 (calculus not required). c. The integral ∫ 0 1 ∫ 0 1 − y 2 e x 2 + y 2 d x d y is easier to evaluate in polar coordinates than in Cartesian coordinates.
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. Let R be the unit disk centered at (0,0). Then ∬ R ( x 2 + y 2 ) d A = ∫ 0 2 π ∫ 0 1 r 2 d r d θ . b. The average distance between the points of the hemisphere z = 4 − x 2 − y 2 and the origin is 2 (calculus not required). c. The integral ∫ 0 1 ∫ 0 1 − y 2 e x 2 + y 2 d x d y is easier to evaluate in polar coordinates than in Cartesian coordinates.
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. Let R be the unit disk centered at (0,0). Then
∬
R
(
x
2
+
y
2
)
d
A
=
∫
0
2
π
∫
0
1
r
2
d
r
d
θ
.
b. The average distance between the points of the hemisphere
z
=
4
−
x
2
−
y
2
and the origin is 2 (calculus not required).
c. The integral
∫
0
1
∫
0
1
−
y
2
e
x
2
+
y
2
d
x
d
y
is easier to evaluate in polar coordinates than in Cartesian coordinates.
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.
Find a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14
and -3x - y + z = −21.
The equation of the plane is:
Determine whether the lines
L₁ : F(t) = (−2, 3, −1)t + (0,2,-3) and
L2 : ƒ(s) = (2, −3, 1)s + (−10, 17, -8)
intersect. If they do, find the point of intersection.
● They intersect at the point
They are skew lines
They are parallel or equal
Answer questions 2
Chapter 16 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Elementary Statistics: Picturing the World (7th Edition)
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