Question

Lim of f(x) as x approaches c- (one sided limits)
f(x)= 3x+9/x^2-9 c=-3

answer is -1/2...how though?

Answer 1

3(x+3)/(x-3)(x+3)

Answer 2

factor, then cancel terms

Answer 3

you're left with f(x) = 3/(x-3), right?

Answer 4

Let's "simplify" our functional expression:$$f(x)=\frac{3x+9}{x^2-9}=\frac{3(x+3)}{(x+3)(x-3)}=\frac3{x-3}$$Now observe what happens when we let \(x\to-3^-\):$$\lim_{x\to-3^-}\frac3{x-3}=\frac3{-3-3}=-\frac36=-\frac12$$

Answer 5

well x = -3

f(-3) = 3/(-3-3) = -1/2

Answer 6

haha got it guys. thank you! i simplified but every time i used the calc it was wrong cuz i forgot that i stored x as a different number before lol. Thanks(:

Answer 7

We have :
\[\Large f(x)=\frac{3x+9}{x^2-9 }=\frac{3(x+3)}{(x-3)(x+3)}=\frac{3}{x-3}\]
So :
\[\Large\lim_{x\to-3}\frac{3x+9}{x^2-9 }=\lim_{x\to-3}\frac{3}{x-3}=\frac{3}{-3-3}=-\frac12.\]