Finding a δ for a Given ε In Exercises 41-46, Find the limit L . Then Find δ such that | f ( x ) − L | < ε whenever 0 < | x − c | < δ for (a) ε = 0.01 and (b) ε = 0.005 . lim x → 6 ( 6 − x 3 )
Finding a δ for a Given ε In Exercises 41-46, Find the limit L . Then Find δ such that | f ( x ) − L | < ε whenever 0 < | x − c | < δ for (a) ε = 0.01 and (b) ε = 0.005 . lim x → 6 ( 6 − x 3 )
Solution Summary: The author explains how to calculate the value of delta and the limit " L" using the following formulas: f(x)=6-x3,
Finding a
δ
for a Given
ε
In Exercises 41-46, Find the limit L. Then Find
δ
such that
|
f
(
x
)
−
L
|
<
ε
whenever
0
<
|
x
−
c
|
<
δ
for (a)
ε
=
0.01
and (b)
ε
=
0.005
.
Find the volume of the solid bounded below by the circular cone z = 2.5√√√x² + y² and above by the
sphere x² + y²+z² = 6.5z.
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y)
is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round
your answer to four decimal places.
1
U
5
4
3
2
1
1
2
5
7
coulumbs
Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an
answer accurate to at least 4 significant digits. Find the volume of E.
Triple Integral
Spherical Coordinates
Cutout of sphere is for visual purposes
0.8-
0.6
z
04
0.2-
0-
-0.4
-0.2
04
0
0.2
0.2
x
-0.2
04 -0.4
Note: The graph is an example. The scale and equation parameters may not be the same for your
particular problem. Round your answer to 4 decimal places.
Hint: Solve the cone equation for phi.
* Oops - try again.
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