
How do I find the limit as approaches negative infinity of ?
Answer
471.9k+ views
Hint: In order to find the solution to this question, we will first convert the term in limits form and then find the limits. We are using limits because infinity is not a number as approaches infinity.
Complete step by step answer:
From the question, we can see that we have been asked to find the value of when approaches negative infinity.
So, to start with the solution, we will first convert the given statement into a mathematical expression. Therefore, we can convert into limits since infinity is not a number.
Therefore, we get:
As we can see above, x approaches to negative infinity, therefore the answer is undefined because is not in the domain of , the limit does not exist.
is undefined.
If the scenario is:
x approaches infinity that is positive infinity, then:
That is the limit of the natural logarithm of when approaches positive infinity is infinity.
We can understand with the help of the following graph:
As when approaches minus infinity:
In this case, the natural logarithm of minus infinity is undefined for real numbers, since the natural logarithm function is undefined for negative numbers:
Therefore, we get:
is undefined.
We can understand with the help of the following graph:
Therefore, we can conclude at this point:
And
is undefined.
Note:
In a hurry, we might end up reading the question wrong and then getting the wrong answer. So, we have to be very careful about that. Also, we can solve this question from the graph of ln x, but sometimes we get confused about the graph, so we have used the conventional method to find the answer.
Complete step by step answer:
From the question, we can see that we have been asked to find the value of
So, to start with the solution, we will first convert the given statement into a mathematical expression. Therefore, we can convert into limits since infinity is not a number.
Therefore, we get:
As we can see above, x approaches to negative infinity, therefore the answer is undefined because
If the scenario is:
x approaches infinity that is positive infinity, then:
That is the limit of the natural logarithm of
We can understand with the help of the following graph:

As when
In this case, the natural logarithm of minus infinity is undefined for real numbers, since the natural logarithm function is undefined for negative numbers:
Therefore, we get:
We can understand with the help of the following graph:

Therefore, we can conclude at this point:
And
Note:
In a hurry, we might end up reading the question wrong and then getting the wrong answer. So, we have to be very careful about that. Also, we can solve this question from the graph of ln x, but sometimes we get confused about the graph, so we have used the conventional method to find the answer.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Explain why it is said like that Mock drill is use class 11 social science CBSE

The non protein part of an enzyme is a A Prosthetic class 11 biology CBSE

Which of the following blood vessels in the circulatory class 11 biology CBSE

What is a zygomorphic flower Give example class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

The deoxygenated blood from the hind limbs of the frog class 11 biology CBSE
