Question

**Calc 2 Help** Describe geometrically the set of points (x,y,z) satisfying the inequalities: 1<= x^2 + y^2 + z^2 <= 4.

Answer 1

I am confused on what the questions is asking.. I understand that this shape is a sphere.

Answer 2

I believe this is something like a sphere with an empty space in it..It's upper limit is : x^2 + y^2 + z^2 = 4..but you have to exclude the points of a sphere which is the: x^2 + y^2 + z^2 <= 1..

So all in all the geometrical result is an "empty" sphere..

Answer 3

What if the equal were to be =1 rather than bounded by 1 and 4, would it be solid then?

Answer 4

if the eqation** sorry

Answer 5

You mean if we had this equation: \[x^2 + y^2 + z^2 = 1\] ?
This would be a sphere with radius = 1

Answer 6

Ok I see.. So would the radius on this problem be sqrt( 4-1)?

Answer 7

I don't think that you should do "4-1"..since the radius is the distance from the origin..
So I would say that the radius is sqrt(4)

Answer 8

We just started vectors and it's a little hard for me to visualize the z plane.. haha

Answer 9

We are having a test on monday on vectors, polar, cylindrical, spherical coordinates and transformations from one system to another, partial derivatives and chain rule!
It's a bit difficult, use paper and pencil to draw them ;)

Answer 10

Ouch.. Which math are you in? I'll be finished w/ calculus after this semester, but start discrete math in the fall. :/

Answer 11

We had discrete math and analysis (calculus) I in the 1st semester..analysis II and linear algebra in the 2nd, in 3rd semester, probabilities and statistics and now numerical analysis and "algorithms and complexity"..I am in the 2nd year, studdying computer science :)

Answer 12

Oh wow.. I'm a CS major too!

Answer 13

good luck on your test

Answer 14

Great :D thank you!