- #1
Metal_Zelda
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Homework Statement
Prove [tex]lim_{x->\frac{1}{10}}\frac{1}{x}=10[/tex]
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
[tex]
\frac{-1}{20}<x-\frac{1}{10}<\frac{1}{20}[/tex]
[tex]\frac{1}{10}<x<\frac{3}{10}[/tex]
[tex]\frac{1}{x}<10
[/tex]
Moving on to the left side of the proof,
[tex]
|\frac{1}{x}-10|<\epsilon[/tex]
[tex]-\epsilon<\frac{1}{x}-10<\epsilon[/tex]
This is where I am stuck. If I use the fact that 1/x<10, I end up with -epsilon<10-10<epsilon, which isn't helpful.