Question

A sporting goods manufacturer designs a golf ball having a volume of 2.48 cubic inches.
(a) What is the radius of the golf ball?
Volume to radius = Pie * radius * length?
v = 4/3 * 3.14 * r3 = 4.18
2.48/ 4.18 = 0.59
Cubed root 0.59 = 0.83872065265271423792386096533889
(b) The volume of the golf ball varies between 2.45 cubic inches and 2.51 cubic inches. How does the radius vary?
The radius varies as a function of the cube root of the volume.
(c) Use the ϵ - δ definition of limit to describe this situation
Identify ϵ and δ = identify epsilon (small Positive number) and lower delta (positive number)
ϵ = f(r) = 4/3 * tt * r3
δ=max(|2.45|),(|2.51|)=?

I had some trouble with this last problem

Answer 1

I'm struggling with the value 4.18. Where did that come from?

Answer 2

v = 4/3 * 3.14 * r3 = 4.18
Volume = 4/3 * pie * radius cubed

Answer 3

That makes no sense. The volume is 2.48. There is no reason for a 4.18 in this problem.

Answer 4

Actually it should be 4/3 * 3.14 = 4.18

Answer 5

Anyway the first two are right. I need help with the last one.

Answer 6

The I go on to Volume(2.48) / 4.18 = 0.59

Answer 7

Then we find the cubed root of 0.59

Answer 8

Which tells us the radius varies as a function of the cube root of the volume.

Answer 9

I am new to using lower delta and epsilon

Answer 10

I know both make for absolute values

Answer 11

\(\dfrac{4}{3}\pi r^{3} = 2.48\)

\(r^{3} = 2.48\cdot\dfrac{3}{4\pi} = 0.592056\)

I'm just not sure what you are doing. It is neither clear nor comprehensible. There is no 4.18 in there. I suppose it is an intermediate result, but you did not show where you obtained it.

Answer 12

Actually it should be 4/3 * 3.14 = 4.18

Answer 13

4/3 * 3.14 = length

Answer 14

length / volume

Answer 15

\(\delta\) is not directly related to 2.45 or 2.51. It is a distance from the limit, so 2.48 - 2.45 = 0.03 and 2.48 - 2.51 = -0.03. Now the absolute values become important.

You wrote this. v = 4/3 * 3.14 * r3 = 4.18
You must see that it is incorrect and should not have been written in this fashion. Very confusing.

This would have been okay:v = 4/3 * 3.14 * r3 = 4.18 * r^3

Answer 16

I agree thank you for pointing it out!

Answer 17

One more thing about that 4.18. You rounded to 2 decimal places. You subsequently posted your result for r to a crazy number of decimal places. This is no good.

How about that delta. Are we clear on what that is. \(\delta\) promises that we will never wander farther from 2.48 than 0.03 in any direction. That's all it means.

Answer 18

so δ = 0.03?

Answer 19

\(0 < \delta < 0.03\)

Answer 20

okay

Answer 21

I might be tempted to use 2.51 and 2.45 and solve for r two more times. This should tell you how far the radius wanders about.

Answer 22

This is where I am confused I never used either of these symbols before I know what they do I just don't know how to apply them.

Answer 23

Just do those two repeat algebra problems.

\(\delta\) promises: If we never wander away more than this, then...
\(\epsilon\) promises that the function never will wander farther than this.

That may be backwards from the usual definition, but I don't find that reversal significant at this point. I could call them Steve and Bob and the idea would be the same.

Answer 24

Okay I think I got it thank you very much for your help I am glad I found this site :)