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1. ### Uniform Convergence of Fourier sine and cosine series

Yes I understand. But if f(x) was continuous in the interval, would my explanation make sense?
2. ### Uniform Convergence of Fourier sine and cosine series

Homework Statement f(x)= {1, ‐1/2<x≤1/2} {0, ‐1<x≤ ‐1/2 or 1/2<x≤1} State whether or not the function's Fourier sine and cosine series(for the corresponding half interval) converges uniformly on the entire real line ‐∞<x<∞ Homework Equations The Attempt at a Solution...
3. ### Showing two sets are equivalent

Damn, y=ex works. Thanks a lot man. Can't believe I didn't think of that.
4. ### Showing two sets are equivalent

But that isn't a bijection as its not one-to-one. For example, -5 maps to 25 and 5 maps to 25. If I can find a bijection from R to R+ ,then I've proven they are equivalent sets. Just can't find the darn bijection.
5. ### Showing two sets are equivalent

Homework Statement Show that R \approx R+ , that is, the set of all real numbers is equivalent to the set of all positive real numbers Homework Equations The only relevent equation is finding one such that F:R\rightarrowR+ is a bijection. The Attempt at a Solution I've...
6. ### Different answers when switching the order of integration

Homework Statement Evaluate the following iterated integrals using the above commands. In each case check your answer by reversing the order of integration in the iterated integral if possible. Homework Equations As a type 1 region: 0<x<1 and x<y<2x \int\int xy2 dy dx As a...
7. ### Homework questions dealing with tangent planes and normal vector

So where is my answer wrong for the first question? I'm still confused...
8. ### Homework questions dealing with tangent planes and normal vector

Hello All, I need help in my Calc 3 class and I decided to come here for homework help. What I'm looking for is someone to just check my work for a couple of homework problems. I've already done the problems, I would just like my work checked. Anyone who helps, your kindness is greatly...
9. ### Joint Density problem again: What am I doing wrong?

Ok I tried it again and this is what I get marginal density of u= Integral (from 0 to u) of 1/u dv. For that I get v/u and I plug in the 0 and u. I am still getting 1. marginal density of v= Integral (from v to 1) of 1/u du. This is ln (u). Plugging in v and 1, I got - ln(v) for my answer...
10. ### Joint Density problem again: What am I doing wrong?

Hello, I would gladly appreciate any and all help with this joint density problem a practice problem for an exam. Please excuse my lack of use of the proper symbols, I don't know how to express them online unfortunately : Joint Density of two random variables, U and V is: f(u,v)= 1/u...
11. ### Can someone check my work for this joint denisty function problem

Homework Statement X and Y have uniform joint density function: f(x,y)= d (constant) for 0<x<1 and 0<y<1-x 1. find d 2. find p(y<x) 3. find cov (x,y) The Attempt at a Solution 1. For this I first graphed x=1 and y=1 and created a square since x can go from 0 to a maximum of 1 and y...