Limit of a function at a point (picture included)

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SUMMARY

The limit of the function |x| at the point x = 0 exists and is equal to 0. While the absolute value function is not differentiable at this point, the limit can be evaluated using the definition of limits. The discussion emphasizes the distinction between differentiability and the existence of limits, clarifying that the limit can still be determined even when a function is not differentiable at a specific point.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with the absolute value function
  • Knowledge of differentiability concepts
  • Basic graph interpretation skills
NEXT STEPS
  • Study the definition of limits in calculus
  • Learn about differentiability and its implications on limits
  • Explore graphical representations of functions and their limits
  • Investigate other functions that are not differentiable at certain points
USEFUL FOR

Students of calculus, mathematics educators, and anyone interested in understanding the concepts of limits and differentiability in functions.

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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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.
 

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