Recent content by lepton123

I know that is the definition for a limit, but I am unsure how to disprove it

Homework Statement Prove that the limit as x approaches 0 of 1/x does not exist Homework Equations Delta epsilon definition The Attempt at a Solution I'm really stuck

Drat, I was hoping that that I wouldn't have to do a case analysis; is there a more elegant way of solving this though?

Homework Statement abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement Homework Equations Triangle inequality? The Attempt at a Solution I have nothing :/

"how much work does the frictional force do on the block?" How do you find this?

Homework Statement Suppose f is continuous on [0,1] and f(0)=f(1). Let n be a natural number. Prove that there is some number x, such that f(x)=f(x+1/n). Homework Equations The hints says to consider g(x)=f(x)-f(x+1/n) The Attempt at a Solution I've tried to consider the function...

What do you mean the work energy theorem? Are you referring to Wnet=change in Kinectic energy, and if so, then the change from the start at the bottom to the end when its at the bottom again? How do I involve friction into this?

Okay, I think I got it now, thanks! I just considered two points; g(1) and g(0), and showed how between those points, there always exists a zero as g(1) can be between 0 and -1 and g(0) is between 0 and 1, so by the intermediate value theorem, there has to be a zero between these two points for...

Okay, I considered doing that; would I try to now show that g(x)=0 for some x?

Homework Statement I have to prove that if a function is bounded for x between (0,1) and f(x) is bounded also between (0,1) and f(x) is continuos that there exists some x such that f(x)=x Homework Equations Intermediate value theorem? The Attempt at a Solution I know that...

Homework Statement A block is projected up an inclined plane that makes an angle θ to the horizontal. It returns to its initial position with half its initial speed. What is the coefficient of kinetic friction between the block and the plane in terms of the angle of the incline...