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What is the limit of as approaches
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Text solutionVerified
Explanation:
To understand why we can't find this limit, consider the following:
We can make a new variable so that .
As , since is undefined. So, we can say that:
As gets bigger, keeps fluctuating between -1 and 1. It never tends towards anything or stops fluctuating at any point.
So, we can say that the limit does not exist. We can see this in the graph below, which shows :
As gets closer to 0, the function fluctuates faster and faster, until, at 0, it is fluctuating "infinitely" fast, so it has no limit.
Final Answer
To understand why we can't find this limit, consider the following:
We can make a new variable so that .
As , since is undefined. So, we can say that:
As gets bigger, keeps fluctuating between -1 and 1. It never tends towards anything or stops fluctuating at any point.
So, we can say that the limit does not exist. We can see this in the graph below, which shows :
As gets closer to 0, the function fluctuates faster and faster, until, at 0, it is fluctuating "infinitely" fast, so it has no limit.
Final Answer
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Question Text | What is the limit of as approaches |
Topic | Limits and Continuity |
Subject | AP Calculus BC |
Class | High School |
Answer Type | Text solution:1 |