Finding the limit of a function as x approaches from the right

[Sky]

lim f(x) = sqrt(x+6) + x
x -> -6+

 

[JeffM]

lim f(x) = sqrt(x+6) + x
x -> -6+

What have you done so far? What techniques are you allowed to use? It is hard to guess where you are stuck if you do not show us your work so far.

 

[Sky]

What have you done so far? What techniques are you allowed to use? It is hard to guess where you are stuck if you do not show us your work so far.

Sorry
Well, I used the substitution technique, but I am not sure if I am allowed to use it since the bidirectional limit is non-existent

Lim(sqrt(x+6) + x) = Lim(sqrt(x+6)) + Lim(x) = -6
x -> -6+ x -> -6+ x -> -6+

 

[stapel]

I used the substitution technique, but I am not sure if I am allowed to use it since the bidirectional limit is non-existent

Check your book and your lecture notes. They'll indicate what you're "allowed" to use.

 

[HallsofIvy]

Note the reason for "limit from the right": \(\displaystyle \sqrt{x+ 6}\) is not a real number for x< 6.