Consider the function f(x)=(2+4e^x)/(2+e^x). a) Show that f(x) is increasing for all x. b) Find the horizontal asymptote on the left and right side.
Use of the lim x->oo to find HA's
The Attempt at a Solution
Seems like an easy question, but it's got me slighty confused. For a) I tried plugging in oo (refer to NOTE at the bottom) for x and solving it that way, but this comes out undefined. Would this be the correct answer or do I need to use another method to prove that f(x) is increasing for all x? For b) I don't know where to start, as I have no idea how to show it has two asymptotes. I was able to find one of the asymptotes (y=4) by factoring e^x out, cancelling it off and then placing in oo, but I don't know how to get the other HA of y=1. Any help would be greatly appreciated, thanks in advance.
NOTE: I used oo to represent infinity since latex wasn't working.