AP Calc AB - Differentials

[michaela_n]

Hey! I'm trying to finish my AP Calculus worksheet for our test tomorrow and I'm having a hard time understanding one of the problems. I would ask someone in the class, but I'm the only junior in AP Calculus and none of the seniors will talk to me! So anyways, heres my issue...

The radius of a sphere is measured to be 3.0 inches. If the measurement is correct to within 0.01 inch, use differentials to estimate the propagated error in the colume of the sphere.

Now, I know a differential equation is an equation that involves an unknown function and its derivative. So for example it's y^l+y = x+3. The unknown function here is y, but I don't know where to go from here. It is a multiple choice problem so the answers are:

a. +/- 0.000001 in³ b. +/- 0.36"pie" in.³ c. +/- 0.036"pie" in.³ d. +/- 0.06 in.³ e. None of these


I'd love any help provided! Thanks!

 

[renegade05]

Hey! I'm trying to finish my AP Calculus worksheet for our test tomorrow and I'm having a hard time understanding one of the problems. I would ask someone in the class, but I'm the only junior in AP Calculus and none of the seniors will talk to me! So anyways, heres my issue...

The radius of a sphere is measured to be 3.0 inches. If the measurement is correct to within 0.01 inch, use differentials to estimate the propagated error in the colume of the sphere.

Now, I know a differential equation is an equation that involves an unknown function and its derivative. So for example it's y^l+y = x+3. The unknown function here is y, but I don't know where to go from here. It is a multiple choice problem so the answers are:

a. +/- 0.000001 in³ b. +/- 0.36"pie" in.³ c. +/- 0.036"pie" in.³ d. +/- 0.06 in.³ e. None of these


I'd love any help provided! Thanks!

You misspelled volume,

but anyway, you don't need to use a differential equation here. A differential has some different meanings but this is a typical type of question in CALC I and they mean to find a linearization at r=3.

The volume of a sphere is \(\displaystyle V(r)=\frac{4 \pi r^3}{3}\).

The change in radius is \(\displaystyle dr=\pm 0.01\)

is this jolting your memory, or setting you in the right direction?