This is a limits question.

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In summary, the limit cannot be found using L'Hopital's rule and is undefined since lnx is not defined for negative numbers. The right handed limit can be found by splitting the limit into two separate limits.
  • #1

Homework Statement


Find the following limit.

Homework Equations


Capture3.JPG

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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  • #2
What is lim(x->0) lnx? What is lim(x->0) 1/x^n?
 
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  • #3
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.
 
  • #4
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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  • #5
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.
 
  • #6
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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What is a limits question?

A limits question is a type of mathematical problem that involves finding the maximum or minimum value of a function as it approaches a specific value or approaches infinity or negative infinity.

Why are limits important in science?

Limits are important in science because they allow us to understand how a system or process behaves as certain variables approach specific values. This information can help us make predictions and understand the behavior of complex systems.

What types of problems can be solved using limits?

Limits can be used to solve a variety of problems in science, including finding the rate of change of a function, determining the maximum or minimum value of a function, and evaluating the behavior of systems as they approach certain values.

How do you solve a limits question?

To solve a limits question, you first need to identify the type of limit (e.g. approaching a specific value, approaching infinity or negative infinity). Then, you can use algebraic techniques, such as factoring and simplifying, or graphical methods, such as graphing the function, to determine the limit value.

What are some real-world applications of limits?

Limits have many real-world applications in fields such as physics, chemistry, and engineering. For example, in physics, limits can be used to calculate the velocity of an object as it approaches a specific point in time, or to determine the maximum capacity of a system. In chemistry, limits can be used to study the rate of chemical reactions as reactants approach certain concentrations. In engineering, limits can be used to analyze the behavior of structures under varying conditions.

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