Recent content by gipc

I think the final answer is still correct, no?

Solve the Integral in cylindrical coordinates ∫∫∫ dxdydz/(sqrt( x^2 + y^2 + (h-z)^2) B Where B is the Ball with a Radius R around (0,0,0), and the parameter h is greater than R. And then infer the average on that ball B with radius R of the distance opposite to the point (0,0,h). I...

Ohh, yes, obviously they are indeed parallel :)

I have the following "Parabolic Dish" z=c(x^2+y^2) I have to prove that all the reflecting light rays that hit that dish go through the same point Q in the Z axis, and then I have to find said point Q. I've thought of reducing the problem to 2 dimensions. Started with the parabola y =...

when i try to take the partial derivatives i can't really take them to x->0 and i get stuck with the epsilon business. The general steps for showing differentiability doesn't really apply here.

I came to a conclusion that f is indeed differentiable. Can someone please help me understand how to prove it? Someone suggested that i use the Taylor expansion but i don't know how to use it. So I'm hoping someone could show me :)

I have: http://img12.imageshack.us/img12/6121/capturerhf.png Is the function differentiable in (0,2)? If so, find its Tangent Plane. So far I have We have (\nabla f)(0,2)=(f_x(0,2).f_y(0,2))=\ldots=(0,1) , so if f is differentiable at (0,2) the only possible differential is \lambda...

But how do you know the series is convergent where f(x)=1.5? It is convergent in [-1,1], how do I take it that there is indeed an x_0 in [-1,1] that satisfies f(x_0)=1.5 and that x_0 is single? Can i take just any random number 123456 and say that there is some x in [-1,1] that satisfy...

Okay, I see, but what guarantees that the solution even exists?

Thanks for all your help. I didn't think checking the endpoints was as easy as just plugging in.One lastquestion, " Finally, if you only need to show that the function exists at 1.5 and -0.5, then that's automatic because the series converges. Explicitly, the function is analytic therefore it is...

What do you mean by "have to check the endpoints of the interval of convergence separately", how precisely do I do that? Sorry but I dodn't remeber the according tool. I though the ratio test was all there is. And the derivative looks good to me... I double checked. d/dx.

I have the ratio test: \displaystyle \frac{(-1)^{n+1}x^{n+1}}{(n+1)^{\frac{3}{2}}}\cdot \frac{n^{\frac{3}{2}}}{(-1)^{n}x^{n}} =\displaystyle \lim_{n\to \infty}\frac{n^{\frac{3}{2}}|x|}{(n+1)^{\frac{3}{2}}}=|x| why does r=[-1,1] and not (-1,1)? And the derivative: f'(x) =...

You are speaking a language I don't understand :( Why does "the max values for f are for even n and min values are for odd n"? And what are "ratios of coeffs", how specifically should I show the sequence is decreasing? And from that, how I deduce the max and min values?I'm sorry for all the...

I don't think at all that I can work with that definition in that case. Maybe work around showing f is single value, I really don't know.

f(x) = \sum_{n=1}^{\infty} \frac{(-1)^nx^{n}}{(n)^{\frac{3}{2}}} Prove f(x) is strictly monotonic (where f is defined) and that there exists one solution to f(x)=1.5 and f(x)=-0.5 First, how do I show that the radius of convergence is between -1 \le x \le 1? And then, how do I...