Recent content by Metal_Zelda

  1. M

    Proving lim_{x->\frac{1}{10}}\frac{1}{x}=10

    I made a few errors in my post as well. I'm going to retype everything I've done, please let me know if I've reached a solution. |\frac{1}{x}-10|<\epsilon \; \; \mbox{when} \; \; |x-\frac{1}{10}|<\delta Let δ=1/20. Then, expanding the left side, we get...
  2. M

    Proving lim_{x->\frac{1}{10}}\frac{1}{x}=10

    Okay, so I took |1/x-10|<epsilon and did \frac{1}{x}-\frac{10x}{x}<\epsilon \frac{1-10x}{x}<\epsilon \frac{-10(x-\frac{1}{10})}{x} <\epsilon -10(x-\frac{1}{10})<\delta, \; \; \mbox{where} \; \; \delta=\frac{1}{20} which leaves me with \frac{1}{200}<x-\frac{1}{10}<-\frac{1}{200} ,Which is...
  3. M

    Proving lim_{x->\frac{1}{10}}\frac{1}{x}=10

    Homework Statement Prove lim_{x->\frac{1}{10}}\frac{1}{x}=10 Homework Equations |f(x)-L|<epsilon, |x-a|<delta The Attempt at a Solution I need to go from 1/x to x, so I applied an initial condition of delta<1/20 \frac{-1}{20}<x-\frac{1}{10}<\frac{1}{20} \frac{1}{10}<x<\frac{3}{10}...
  4. M

    Polynomial Long Division for Limit Calculation

    Sorry, I forgot about the -a^5. I got it now, thanks!
  5. M

    Polynomial Long Division for Limit Calculation

    I'm not seeing the cancellation. Could you elaborate?
  6. M

    Polynomial Long Division for Limit Calculation

    Homework Statement \frac{x^5-a^5}{x^2-a^2}, where a is some constant. Homework EquationsThe Attempt at a Solution I can't figure out how to do this with long division. With synthetic, I can get to \frac{a^4+a^3 x+a^2 x^2+a x^3+x^4}{a+x} x^3+xa^2+...