Question

Find delta if epsilon is 0.03. The formula is ((4/3)pi(r)^3).

Answer 1

What is your definition of epsilon and delta here? I know what I typically means, but it's not clear how that applies in this context.

Answer 2

A sporting goods manufacturer designs a golf ball having a volume of 2.34 cubic inches.
(a) What is the radius of the golf ball? (Round your answer to four decimal places.)
in

(b) If the ball's volume can vary between 2.31 cubic inches and 2.37 cubic inches, how can the radius vary? (Round your answers to four decimal places.)
< r <

(c) Use the ε-δ definition of limit to describe this situation.
lim




= 2.34
r →


Identify ε and δ. (Round your answers to four decimal places.)
ε =
δ =

Answer 3

So the way it's set up is volume of the sphere (4/3)(pi)(r^3) is the limit and equals 2.34. r=0.8236

so epsilon = 0.03 because of the difference between 2.37 and 2.34.

delta is supposed to equal 0.0033 but I can't get the calculator to do that .

Answer 4

In this case, the variance in the function f(r) = 4pi/3.r^3 is +/- 0.03 around 2.34 cubic inches. This is the epsilon. Now you need to find what values of r give 2.31, 2.37 and 2.34 and compare the first two against the limit answer 2.34. The maximum of those two variances in r is your delta. Make sense?

Answer 5

So the 0.8201 for 2.31 and the 0.8271 for 2.37 are part of the delta?

Answer 6

What is r for Volume = 2.34? Then compare that value of r with the two you just calculated.

Answer 7

0.8236. then do I add or subtract like 0.8271-0.8236?

Answer 8

call those other two values of r, r1 and r2. Call the value of r for the exact volume the 'perfect r', rp.
Then delta = max(|r-r1|, |r-r2|)

Answer 9

I mean delta = max(|rp-r1|, |rp-r2|)

Answer 10

so delta equals 0.0035. That makes way more sense.

Answer 11

give me a 'good answer' if you can ;-)

Answer 12

\[ \delta=\max(\left| 0.8236-0.8201\right|),(\left|0.8236-0.8271 \right|)=0.0035\]

Answer 13

Yeah?

Answer 14

I'm not going to check the numbers but this looks right, yes.

Answer 15

Thank you so much for your help!!! My calc book does not explain anything. I appreciate it :D