Recent content by cantRemember

  1. C

    Graduate Do purely electrostatic ion traps exist?

    I was wondering whether you could trap a cation simply by putting it inside a positively charged sphere. Is this possible?
  2. C

    Undergrad How to find error between non-linear plot and data points?

    Is there a formal way to measure the error between some arbitrary points and a non-linear curve in order to minimize it?
  3. C

    Undergrad Why won't standard curve length function work in semi-circle?

    They can go to ±∞ (i.e. ln(x)''=(1/x)'=-(1/x^2) and as x→0, f '' (x) → -∞ Besides that, you can think the parametric plots as "trajectories", the point x,y moves as time proceeds. The derivative dx/dt would (probably) be the x-coordinate "speed", while d^2x/dt^2 would be it's x-axis...
  4. C

    Undergrad Why won't standard curve length function work in semi-circle?

    Thanks, this was useful.
  5. C

    Undergrad Why won't standard curve length function work in semi-circle?

    The proof of "en.wikipedia.org/wiki/Arc_length#Finding_arc_lengths_by_integrating" requires that the f '(x) is continuous in the closed interval [a,b] And x→r f '(x)→ -∞ so f '(x) is not continuous at x=±r (Plot) Also see This
  6. C

    Undergrad Why won't standard curve length function work in semi-circle?

    The integral can be solved indeed, but if you try to evaluate it for x=-r to r (i.e. the entire semi-circle) you get something.. ugh... undefined (∞-∞ or similar). This is why (I guess) Wolfram Alpha lagged, having trouble to calculate such a definite integral. Thanks for your assistance.
  7. C

    Undergrad Why won't standard curve length function work in semi-circle?

    You are correct. I should test for derivative's continuity first.
  8. C

    Undergrad Trigonometric Inverse Substitution: How do we know which substitutions to use?

    This contains most methods involving trigonometric substitution, and probably is the most usefull calculus reference sheet I have ever found. Link.
  9. C

    Undergrad Why won't standard curve length function work in semi-circle?

    Ok, so for a give function f(x) it's curve length from a to b is supposed to be ∫(1+(f '(x))^2)dx evaluated from a to b. However even wolfram alpha had a hard time solving that, plus the results were wrong. What am I missing? PS: With f(x)= sqrt(r^2-x^2)
  10. C

    Undergrad Weightless Vacuum Container maximum height

    Assume you have a weightless constant volume container "filled with" vacuum. If you let it float in the atmosphere, how "high" would it go? I guess at some point Archimedes' principle should fail. What do you think?
    • cantRemember
    • Thread
    • Container Height Maximum Maximum height Vacuum
    • Replies: 1
    • Forum: Mechanics
  11. C

    Can't use a simple integral properly-must be retarded

    Thank you. But how can you define density in segments while you cannot define mass?
  12. C

    Can't use a simple integral properly-must be retarded

    I will show you my (obviously wrong) way of thinking when i have to apply an integral. Please correct me where I'm wrong. (imaginary question) Suppose you have a mass distribution across a line, where the mass of each point is given by the equation f(x)=a*x (assume a is a constant) find...
  13. C

    Undergrad Failure to understand a basic integral application

    I will show you my (obviously wrong) way of thinking when i have to apply an integral. Please correct me where I'm wrong. (imaginary question) Suppose you have a mass distribution across a line, where the mass of each point is given by the equation f(x)=a*x (assume a is a constant) find...