Question

How do you find `lim (x+5)(1/(2x)+1/(x+2))` as `x->0^+` using l'Hospital's Rule or otherwise?

Answer 1

The limit is plus infinity. See explanation.

Explanation:

`lim_{x->0^+}[(x+5)(1/(2x)+1/(x+2))]=`

`=lim_{x->0^+}[x/(2x)+x/(x+2)+5/(2x)+5/(x+2)]=+oo`

From the sum in the second line the first two expressions coverge to `1/2` and `0` respectively, the last two expressions diverge to `+oo`