Why are we allowed to do this? v. limits

[ggcheck]

lim(e^(lnx)) as x---> inf. = e^(lim(lnx) as x--->inf.)

the book just says "by continuity of e^x"

why are we allowed to do this?

 

[Ben Niehoff]

You can prove it using the definition of a limit. The continuity of e^x turns out to be important in the proof.

 

[ggcheck]

this isn't an actual homework problem; I ran into this while reading the book... it doesn't elaborate any further

 

[Hurkyl]

Refer back to your limit laws; you learned limits of sums, limits of products, et cetera. One of them was limits of compositions.