Recent content by sara_87

Homework Statement Find the limit as n tends to \infty of: \frac{(-1)^n}{n} Homework Equations The Attempt at a Solution I know that (-1)^n alternates between 1 and -1. I also know that the limit of 1/n is 0. But I don't know how to compute the above limit. Any ideas will...

oh right i see. thank you.

Homework Statement MATLAB uses double precision as default. How can I change this to single? so that all computations will be made using single precision. Homework Equations The Attempt at a Solution I went to: file preferences virtual reality precision: floating point...

thank you very much for these ideas. well, I don't want to use another language, I would like to stick with MATLAB. the symbolic toolbox can use higher precision using vpa for example: vpa(pi,40) will use 40 significant figures, however, the problem is: the outcome will be a symbol and i want...

oh right i see. With what precision is pi calculated? double precision? also, with other functions such a sine, cosine, log, are they also calculated with double precision? thank you

Homework Statement The precision in MATLAB is approximately 2*10^(-16), is there a way that my computations can be calculated using a smaller precision? Homework Equations The Attempt at a Solution if i want to calculate the sum of pi^2*j where j=1:20 but i want it to be...

I found this post useful. Just one question: this is a 2-d problem where the eigen-values of the jacobian were used to determine the type of linear stability of the steady states. Can such a technique be used for a 3-dimensional system? If so, do we require ALL 3 eigenvalues to be of the same...

Homework Statement I have attached a picture including 2 equations: (2.13) and (2.14) I don't understand how they got from (2.13) to (2.14) using integration by parts Homework Equations The Attempt at a Solution For the integral: \int_{\tau_0}^t\sigma(\tau)d\tau=...

Homework Statement I have 2 graphs in latex, side by side, that were attached using: \includegraphics I want to draw an arrow going from the middle of the first graph to the middle of the second graph. Homework Equations The Attempt at a Solution I tried using the tikz package...

Thank you all for these ideas. I find what HmBe said very interesting: ''Well I suppose you could cheat a little, showing that f'(0)=0 and that f(0)=0 (which you've already done) shows there is a repeated root at x=0, then you don't have to solve anything. and because the root is...

But, we have to assume that we don't know that x=1 is a root of the function.

Thank you. but the derivative at 0 is =0. how would absolute monoticity help?

Oh right, i see. If we assume we have a different function that IS continuous in (0,2) and that the IVT does apply, then we can use that f(0)=0 and f'(0)=0 But, what do you mean by: ''because the root is quartic can only have one more root''?

Yes, I think that's what we are supposed to do. but, how does showing that f'(0)=0 and that f(0)=0 show that there is a repeated root at x=0?

Yes, the function is even since f(-x)=f(x) (since x appears only as x^2). But, I don't understand the next part: The derivative is f'(x)= -4 x \left(1-x^2\right)-\frac{-x \left(1-x^2\right)-2 x \left(1-\frac{x^2}{2}\right)}{2 \sqrt{\left(1-x^2\right) \left(1-\frac{x^2}{2}\right)}}...