Thread: find 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?

This is nearly impossible to read...

Is it



or

?

thats how it is i dont know how to do a not equal sign

Originally Posted by dat1611

fify

Originally Posted by dat1611

thats how it is i dont know how to do a not equal sign

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

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ok can someone help with the actual problem

Do you know L'Hopital's rule? If you do, just apply to the numerator and denominator and it ' should be pretty easy.

Hello, dat1611!

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: .

so
= 1
so the answers 1?

Yes!Although, it seems like you don't quite understand why. Do you need help with that?