I am doing these practice problems to study for a test and I just can't figure them out, it's kind of frustrating.(adsbygoogle = window.adsbygoogle || []).push({});

The first concerns the delta-epsilon proof.

f(x) = 2-(1/x)

x is approaching 1, and the limit is 1.

Epsilon is given at 0.1

so, what I have...

0<|x-1|<d (delta)

|f(x)-1|<.1

so

|2-(1/x)-1|<.1

|1-(1/x)|<.1

Maybe I am just an idiot, but how do I go from there?

The answer is delta=1/11, I just can't see how to get it...

I mean, I have done other problems like it,

like for lim x->3 (2x-5) L=1 e=.01

|2x-5-1|<.01

2|x-3|<.01

|x-3|<.005 so delta=.005

And this other problem:

find the limit, using algebra, for x->0 of sin7x/sin9x

I multiplied both sides by csc9x, to get (sin7x*csc9x)/1

because sinx*cscx=1, sin9x*csc9x=1

But I can figure out where to go from there.

Am I doing it wrong?

Thank you for any help!

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# Homework Help: Need some help with limits

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