Limit of a function, using L'hop: lim[x->infty] x - ln x

[grapz]

Lim x --> infinity x - lnx

The question says to use L'hopital rule but i guess you can use any method you want.

This is in the form of infinity - infinity.

so i have to somehow convert this into the form 0/0 or infinity/ infinity. but how do i do it in this case?

 

[pka]

Re: Limit of a function, using L'hop

\(\displaystyle y = x - \ln (x)\; \Rightarrow \;e^y = e^{x - \ln (x)} = e^x e^{ - \ln (x)} = \frac{{e^x }}{x}\)