Math Is Fun Forum

Ok done. First in all. Im gonna wait till someone beats me on one and then focus on that one etc.

I have no life

Why doesnt my highscore (and therefore 1st place) of the add single, show in "my" page.

http://www.mathopolis.com/user.php?u=luisrodg

Since theres a theorem that says:

From the limits of integration you need to get the domain of integration and then from that domain setup a new double integral but with the other order.

Well, I'd love to take a look but I havent taken any analysis class so im lost as to where to start. Hopefully that changes next semester when I will take Advanced Calculus.

Also, the proof of continuity deals with analysis, the exercise of finding the K is from Calc1. How come?

OFF-TOPIC:

Ricky, I always wondered what Real Analysis was, is that the same as Advanced Calculus?

Well, it is true that back in Calc1 we were told that the sum and product of continuous function are continuous. But one thing is to take it for granted and another thing is to actually prove it which was what Wizard asked. Right?

In what class are you mentioning?

I wouldnt know how to prove the first one is continuous. I always took for granted all polynomials are continuous. Maybe to prove it you need to use epsilon-delta proofs?

For the second one, the question states to find K such that the piece-wise function f is continuous at x=2. For f to be continuous the sided limits need to be the same and they need to be equal to f(2). So we need the limit as x approaches 2 from the left to be equal to the limit as x approaches 2 from the right.

So we take the limit from the left and we get 4k and we take the limit from the right and we get 4 + k. For the function to be continuous then those two need to be equal. So:

4k = 4 + k
3k = 4
k = 4/3

So now that we know k=4/3 then the limit from the left equals 16/3, from the right equals 16/3 and f(2) = 16/3. So we found our k such that f is continuous.

Isnt the commutative law a set identity itself?

Find the gradient of the surface and this vector will be normal to the surface. Having this normal vector you can find the tangent plane and also find the normal line.

Another way is to note that the vector:

Will be normal to the surface. So repeat above steps.

I like the adding game

I put up a nice highscore for you all to beat