What is the limit of lnx as x approaches a negative number?

[Nipuna Weerasekara]

Homework Statement

Find the following limit.

Homework Equations

The Attempt at a Solution

I cannot apply L' Hopital rule because it does not apply to this question. Hence I have no idea how to approach to this question. Please give me some guidelines.

 

[member 587159]

What is lim(x->0) lnx? What is lim(x->0) 1/x^n?

 

[Nipuna Weerasekara]

What is lim(x->0) lnx? What is lim(x->0) 1/x^n?

I already know the answer to this and it is zero but I do not know how it comes.
For your question, lim (x->0) lnx is infinity and lim(x->0) 1/x^n is again infinity.
But I do not find any help from these two.

 

[member 587159]

I already know the answer to this and it is zero but I do not know how it comes.
For your question, lim (x->0) lnx is infinity and lim(x->0) 1/x^n is again infinity.
But I do not find any help from these two.

The answer is not zero.
And more specifically, what kind of infinity are the limits above I asked for? I also forgot to mention the following very important thing: lim(x->0) lnx is NOT defined. The right handed limit is defined though.

 

[Nipuna Weerasekara]

The answer is not zero.
And more specifically, what kind of infinity are the limits above I asked for? I also forgot to mention the following very important thing: lim(x->0) lnx is NOT defined. The right handed limit is defined though.

I think The question has some printing mistake or so. However thanks for your kind concern.

 

[member 587159]

I think The question has some printing mistake or so. However thanks for your kind concern.

The answer is that the limit does not exist since lnx is undefined for negative numbers. The right handed limit can be obtained by splitting the limit in 2 separate limits by using lim x>a fg = (lim x>a f )*( lim x>a g).