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

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SUMMARY

The limit of the natural logarithm function, ln(x), as x approaches a negative number is undefined. Specifically, as x approaches zero from the right, ln(x) approaches negative infinity, while the limit of 1/x^n also approaches infinity. The discussion clarifies that the limit does not exist for negative inputs, emphasizing that the right-handed limit can be evaluated by separating the limit into two distinct parts using the product of limits rule. The conclusion is that ln(x) is not defined for negative values.

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Homework Statement


Find the following limit.

Homework Equations


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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.
 
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What is lim(x->0) lnx? What is lim(x->0) 1/x^n?
 
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Math_QED said:
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.
 
Nipuna Weerasekara said:
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.
 
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Math_QED said:
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.
 
Nipuna Weerasekara said:
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).
 
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