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...
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...
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}...
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+...