Recent content by peace-Econ

SammyS Sorry, which part you're asking? Is it for what Trevor Vadas said? I'm now just wondering how I can conclude this problem from |√(f(x)) - √(R)|^2 < |√(f(x)) - √(R)||√(f(x)) + √(R)| = |f(x) - R| < ε^2.

Thank you for your help. But, sorry, how can I conclude this? Why can I say that lim x->a sqrt{f(x)}=sqrt{R}?

Yes, you're right.

I actually don't know what it is...I just don't know how to proceed. Could you help me how I get to start with this question?

Homework Statement Suppose that f(x)>=0 in some deleted neighborhood of c, and that lim x->a f(x)=R. Prove that lim x->a sqrt{f(x)}=sqrt{R} under the assumption that R>0. Homework Equations if 0<|x-c|<delta, then |f(x)-L|<epsilon. The Attempt at a Solution I don't know how to...

actually, I think I made it. Thanks!

Sorry. the integral is actually 1 to 0. This question is actually induction. Integral(1-0): (x^m)*(1-x)^k=n!/(k+1)(k+2)...(K+m+1) where m is a nonnegative integer and k > -1 So, I thought that if I take integral from the right side, I can prove it. But it does not seem the case...

Homework Statement Solve the integral. Homework Equations Integral: (x^m)*(1-x)^k where m is a nonnegative integer and k > -1 The Attempt at a Solution I've tried to take this integral by using integral by parts, but I couldn't take it. Can anyone tell me how to take this...

If an arbitrary unbounded set + another arbitrary unbounded set, is it also going to be an unbounded set?

Homework Statement Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions. Homework Equations The Attempt at a Solution

You're right. I was just working on the characteristic equation. But, I could figure it out. Thank you so much!

Homework Statement Factor the equation. Homework Equations x^3-2x^2-5x+6 The Attempt at a Solution Could someone help me know how to factor this equation?

Homework Statement Find a particular solution for these second order differential equations. Homework Equations 1) y''+9y=tan3t 2) y''+y=tan^2t The Attempt at a Solution I want to find a fundamental solutions y1 and y2 because I want to find a particular solution like this...

sorry, you're right. The theorem I was trying to use is that if f and its partial derivative is continuous on the rectangle containing the given initial value problem, we can say that it has a unique theorem.

Did you mean that my way and answer is wrong? This problem should be verified by using the theorem of uniqueness. I got y(t)=(4x^2)-64. Then can i say that this is a unique solution?