Question

how do i find the the lim as x goes to 0 of ln(x^2-9)

Answer 1

well, ln(x) is only defined if the argument x is greater than zero.

Clearly for x near to zero, x^2 - 9 < 0, i.e., x^2 - 9 is negative. Hence ln(x^2 - 9) is undefined.

Therefore this limit doesn't exist. Make sense?

Answer 2

yea somewhat thanks

Answer 3

More precisely
ln(x^2 - 9) has a domain of |x| > 3, i.e., x < -3 and x > 3.

Hence the limit of ln(x^2 - 9) as x --> 0 cannot exist, as the function is not defined in a neighborhood around x = 0.