Question

prove the statement using the Epsilon Delta Limit Definition
lim x--1 1/x=1/2

Answer 1

\[\large\lim_{x\rightarrow 1}\frac{1}{x}=\frac{1}{2}\]Can't be proven because it isn't the case. \(1/1=1\)

Answer 2

what

Answer 3

You wrote the problem down incorrectly or something.

Answer 4

\[\lim_{x \rightarrow 2}\frac{ 1 }{ x }=\frac{ 1 }{ 2}\]

Answer 5

sorry that is question

Answer 6

So you have to show that:\[\forall \epsilon\ \exists \delta\ \ 0<|x-(2)|<\delta \Rightarrow |\frac{1}{x} - \left(\frac{1}{2}\right)| < \epsilon\]

Answer 7

prove

Answer 8

that step i know

Answer 9

i wanna to know what next

Answer 10

You want to get it into the form for the epsilon equation |x-2|

Answer 11

\[\left|\frac{2-x}{2x}\right|<\epsilon\]\[\left|\frac{-1}{2x}\right||x-2|<\epsilon\]

Answer 12

Then you divide by the delta equation

Answer 13

\[\left|\frac{-1}{2x}\right| < \frac{\epsilon}{\delta}\]

Answer 14

\[ \delta < |-2x|\epsilon \]This seems sufficient, doesn't it?

Answer 15

oops, you wanna get rid of the -2x somehow