Question

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

Answer 1

Substitution.

Explanation:

Nothing becomes undefined or indeterminate, so use substitution.

`lim_(xrarr1)(x+5)(1/(2x)+1/(x+2)) = 6(1/2+1/3) = 3+2=5`