f(x)= ln x/(x-1), if 0<x not =1

c , if x=1

and what kind of discontinuity is present if c does not have this value?

can someone help me with this problem?

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- August 2nd 2010, 12:39 PMdat1611find the value for which the function is continuous
f(x)= ln x/(x-1), if 0<x not =1

c , if x=1

and what kind of discontinuity is present if c does not have this value?

can someone help me with this problem? - August 2nd 2010, 04:40 PMProve It
This is nearly impossible to read...

Is it

or

? - August 3rd 2010, 12:44 PMdat1611

thats how it is i dont know how to do a not equal sign - August 3rd 2010, 12:54 PMskeeter
- August 3rd 2010, 01:45 PMVlasev
It is done by \neq

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For the question at hand, you need to determine a value c such that the function is continuous. One way could be to just plug in 1 in the above definition with the natural log, but you cannot do that since you'd get something of the form 0/0. Hence you need to find the limit of [LaTeX ERROR: Convert failed] as x approaches 1. Or more succinctly, find

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Once you find that, you can just set c equal to it. From the definitions of continuous functions, f(x) is continuous at point a if

[LaTeX ERROR: Convert failed] - August 3rd 2010, 01:46 PMdat1611
ok can someone help with the actual problem

- August 3rd 2010, 01:56 PMVlasev
Do you know L'Hopital's rule? If you do, just apply to the numerator and denominator and it ' should be pretty easy.

- August 3rd 2010, 02:13 PMSoroban
Hello, dat1611!

Quote:

Find the value of for which the function is continuous.

To be continuous at , we want: .

The left side goes to so we can apply L'Hopital.

.

Therefore: .

- August 3rd 2010, 02:21 PMdat1611
so

= 1

so the answers 1? - August 3rd 2010, 02:28 PMVlasev
Yes!Although, it seems like you don't quite understand why. Do you need help with that?