limit as x approaches -3 from the left (x+2) / (x+3)

Question

Hi,

 I know that if I  plug (-3) in "x", the denominator will be 0, but if I plug a number less than -3; like -4, it'll be 2. I'm not sure if this's right and how to graph this.

 

Thanks in advance

Answer 1

(x+2)/(x+3)=((x+3)-1)/(x+3)=1-1/(x+3).

Let x=-3-Δ, where Δ is small and positive, then x+3=-Δ and (x+2)/(x+3)=1+1/Δ.

Therefore as Δ→0, (x+2)/(x+3)→+∞. So the left limit is infinity (positive).

(The right limit is -∞.)