Limit of a function at a point (picture included)

So, in summary, the limit of the function at 0 is 0, even though the function is not differentiable at that point.
  • #1
maplesyrup23
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I'm trying to find the limit of this function at 0.

I know that for the abs (x) graph, 0 is not differentiable because of abs (h)/h, but I'm not certain about the point on this function.

There is no function given, only the picture.

Thanks in advance!
 

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  • #3
maplesyrup23 said:
I'm trying to find the limit of this function at 0.

I know that for the abs (x) graph, 0 is not differentiable because of abs (h)/h, but I'm not certain about the point on this function.

There is no function given, only the picture.

Thanks in advance!
It's true that |x| is not differentiable at x = 0. However, limx→0 |x| exists, and is equal to 0.
 

1. What is the limit of a function at a point?

The limit of a function at a point is a value that the function approaches as the input (x) approaches a specific value. It is also known as the 'y-value' of the function at that point.

2. How is the limit of a function at a point calculated?

The limit of a function at a point is calculated by evaluating the function at values of x that are very close to the given point. This can be done algebraically or graphically.

3. What does it mean if the limit of a function at a point does not exist?

If the limit of a function at a point does not exist, it means that the function does not approach a specific value as the input approaches that point. This could be due to a jump or discontinuity in the function.

4. Can the limit of a function at a point be different from the actual value of the function at that point?

Yes, the limit of a function at a point can be different from the actual value of the function at that point. This can happen when the function has a removable discontinuity or a hole at that point.

5. How can the limit of a function at a point be used in real life?

The limit of a function at a point can be used in real life to analyze the behavior of a system or process. For example, it can be used to predict the future value of a stock or the maximum temperature a machine can reach.

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