Volumes of solids . Find the volume of the following solids using triple integrals. 24. The solid in the first octant bounded by the cone z = 1 − x 2 + y 2 and the plane x + y + z = 1
Volumes of solids . Find the volume of the following solids using triple integrals. 24. The solid in the first octant bounded by the cone z = 1 − x 2 + y 2 and the plane x + y + z = 1
Volumes of solids. Find the volume of the following solids using triple integrals.
24. The solid in the first octant bounded by the cone
z
=
1
−
x
2
+
y
2
and the plane x + y + 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.
4
In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and
evaluate the integral. Hint: Find the limits on r and s by sketching the area of integration in the (x, y) plane along
with the r and s axes, and then show that the same area can be covered by s from 0 to r and r from 0 to 1.
7. What are all values of 0, for 0≤0<2л, where 2 sin² 0=-sin?
-
5π
6
π
(A) 0, л,
and
6
7π
(B) 0,л,
11π
, and
6
6
π 3π π
(C)
5π
2 2 3
, and
π 3π 2π
(D)
2' 2'3
, and
3
4元
3
1
די
}
I
-2m
3
1
-3
บ
1
#
1
I
3#
3m
8. The graph of g is shown above. Which of the following is an expression for g(x)?
(A) 1+ tan(x)
(B) 1-tan (x)
(C) 1-tan (2x)
(D) 1-tan
+
X
-
9. The function j is given by j(x)=2(sin x)(cos x)-cos x. Solve j(x) = 0 for values of x in the interval
Quiz A: Topic 3.10
Trigonometric Equations and Inequalities
Created by Bryan Passwater
can you solve this question using the right triangle method and explain the steps used along the way
Chapter 16 Solutions
Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
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