Question

How do I find the limit as x approaches negative infinity of lnx?

Answer 1

Answer:

Step-by-step explanation:

since ln x is Only defined for x > 0 , then x CANNOT approach negative infinity. This there is no meaning about talking of the limit then.

Answer 2

In the Real Plane with real x and y coordinates, logarithm of non positive numbers is not being defined.

However in the 4 Dimensional Complex space considering the real and imaginary parts of both x and y coordinates , logarithm of all positive, negative numbers and other non-zero non real complex numbers are defined.

$\\ \sf \lim_{x \to - \infty }( \ln(x)) = \lim_{x \to + \infty }( \ln( - x))$

$\\ = \lim_{x \to + \infty }( \ln( - 1) + \ln(x))$

$\\ = \lim_{x \to + \infty }( \ln(x)) + i\pi$

So, the limit's real part diverges however; its imaginary part is a constant.

$\to + \infty + i\pi$

where, i² = –1