Continuous on an open interval?

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SUMMARY

The functions t², -2t, and 2 are all continuous on any open interval. This conclusion is based on the established mathematical principle that all polynomial functions are continuous across their entire domain, which includes open intervals. Therefore, these specific functions do not present any discontinuities when evaluated over any range of t values.

PREREQUISITES
  • Understanding of polynomial functions
  • Knowledge of continuity in calculus
  • Familiarity with open intervals in mathematics
  • Basic comprehension of limits and theorems related to continuity
NEXT STEPS
  • Study the properties of polynomial functions and their continuity
  • Learn about the definitions and implications of open intervals in calculus
  • Explore theorems related to continuity, such as the Intermediate Value Theorem
  • Review examples of continuous and discontinuous functions for practical understanding
USEFUL FOR

Students studying calculus, mathematics educators, and anyone seeking to deepen their understanding of function continuity and polynomial behavior.

bhsmith
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Homework Statement



Is t^2, -2t and 2 continuous on an open interval?

Homework Equations



I have re read the theorems and explanations of how something is continuous but i still don't understand it.

The Attempt at a Solution

 
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bhsmith said:

Homework Statement



Is t^2, -2t and 2 continuous on an open interval?

Homework Equations



I have re read the theorems and explanations of how something is continuous but i still don't understand it.

The Attempt at a Solution


Yes. Any polynomial is continuous on an open interval.
 

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