Recent content by lineintegral1

The substitution u=r^2 would be significantly easier to deal with. One can then use parts or another substitution to make the integral elementary.

Wow, okay, so that makes it obvious. Thanks for the help guys, I appreciate it. Neat stuff!

Problem: Let L and M be finite dimensional linear spaces over the field K and let g: L\times M \rightarrow K be a bilinear mapping. Let L_0 be the left kernel of g and let M_0 be the right kernel of g. a) Prove that dim L/L_0 = dim M/M_0. b) Prove that g induces the bilinear mapping g': L/L_0...

Well, if p \in (E')^c , then it is not a limit point. Thus, there exists a neighborhood around p that does NOT contain any points of E. Your job is to make the radius of this neighborhood sufficiently small so that this occurs. How does this imply that the set is open? Another option is to...

Um, p-iterations of L'Hospital's rule would be much clearer, I think. The limit is certainly 0, but I think you are making it more complicated than it needs to be.

I think this question has been asked like a dozen times in the past two months. I'm surprised you didn't find it doing a quick google (if you did that). My hint for you is to consider the derivative of ||c(t)||^2. How do you determine the derivative of a dot product? And how do dot products...

I think you'll find that, for any line you choose to approach the origin with, you'll get a single variable limit of 0/0 form. You may apply L'Hospital's Rule for this. Remember that L'Hospital's Rule only works for single variable limits. If you are having difficulty getting differing...

You are correct, the integral formula does not converge if the real part is less than one. This is why it is useful to use the analytic continuation of the gamma function. In other words, we can a way to extend the domain of the gamma function. Take a look at the following for more...

Another way to go about it is to show that the contrapositive is true. You are saying that if a^2 is divisible by 3, then so is a. The contrapositive is that if a is not divisible by 3, then a^2 isn't either. If a is not divisible by 3, how can it be written? Can you think of a way to write...

Actually, the original differential equation is separable. Try separating and integrating accordingly. After all, your right hand side is a function only of x.

Sorry, I'm still a little stuck here, are you just saying find any map with those properties? Is there a particular one I'm looking for? Or is it arbitrary? Again, I'm still trying to figure out how these quotient spaces work. How can I find such a map whose kernel relates to the...

Hey all, We have not covered quotient vector spaces in class, but my homework (due before next lecture) covers a few proofs regarding quotient spaces. I've done some reading on them and some of their aspects, but as it is still a new concept, I am struggling with how to go about this proof...

This is a great start at jotting down the important information. You are now ready to solve the problem. You already stated that, ||\vec{r}||^2=\vec{r}\cdot\vec{r} So, if you can show that the derivative of the magnitude squared is zero everywhere, then the magnitude is constant. If it is...

Yup! Draw a picture if it helps, but this should be evident from daily experiences. What the positive answer is saying, of course, is that the length of the bottom leg of the triangle is increasing.

You need to solve for h at the given instant in time (you can do this easily given the Pythagorean relationship; this should involve no differentials). Also, note that the length of the ladder does not change at all as time progresses. Therefore, \frac{dL}{dt} will be zero. Also, there is an...