What Happens to ln[(x+2)/(x-1)] as x Approaches -2 from the Left?

[gillgill]

i have done part of the work
but i got stuck here

what is
lim f(x) = lim ln [(x + 2)/(x - 1)] =?
x→-2- x→-2-

how do u solve for this?

 

[VietDao29]

What is:
$$\lim_{x \rightarrow -2 ^ -} \frac{x + 2}{x - 1}$$? Note that the numerator tends to 0, while the denominator tends to -3.
Then what can you say about:
$$\lim_{x \rightarrow 0 ^ +} \ln x$$?
Viet Dao,

 

[gillgill]

that would be -infinity??

how about
lim f(x) = lim ln [(x + 2)/(x - 1)] =?
x→-2+ x→-2+

 

[Diane_]

Obviously, the numerator and denominator will separately approach the same values, so the ratio will also approach the same value. However, notice that in this case, the numerator will always be positive while the denominator will be negative. What does that tell you about the ratio? And what happens when you take the natural log of such a quantity? So, what can you say about the function when you try to take this limit?