Help understanding what limits are

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SUMMARY

The discussion focuses on evaluating the limit of the function lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x). The initial attempt resulted in an indeterminate form of 0/0 when substituting x = 2. The correct approach involves factoring both the numerator and denominator to resolve the limit, leading to the final answer of 1/8. This highlights the importance of recognizing and addressing indeterminate forms in calculus.

PREREQUISITES
  • Understanding of limits in calculus
  • Knowledge of factoring polynomials
  • Familiarity with indeterminate forms
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the concept of L'Hôpital's Rule for resolving indeterminate forms
  • Learn more about polynomial long division
  • Explore the properties of limits involving rational functions
  • Practice additional limit problems involving factoring
USEFUL FOR

Students studying calculus, particularly those struggling with limits and indeterminate forms, as well as educators looking for examples to illustrate these concepts.

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Homework Statement


http://www4c.wolframalpha.com/Calculate/MSP/MSP18091a03ad70feibdhb300005da572897hebg236?MSPStoreType=image/gif&s=52&w=143&h=42


Homework Equations


lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x)


The Attempt at a Solution


I plugged in 2 for x and it was 0/0 so then I divided each term by the highest power, which is x^3 but I still got 0/0. The answer is 1/8 but I don't know how to get it.
 
Last edited by a moderator:
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azncocoluver said:

Homework Statement


http://www4c.wolframalpha.com/Calculate/MSP/MSP18091a03ad70feibdhb300005da572897hebg236?MSPStoreType=image/gif&s=52&w=143&h=42


Homework Equations


lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x)


The Attempt at a Solution


I plugged in 2 for x and it was 0/0 so then I divided each term by the highest power, which is x^3 but I still got 0/0. The answer is 1/8 but I don't know how to get it.

Factor the numerator and denominator!
 
Last edited by a moderator:


Oh yeah! I totally forgot about that. Thank you!
 

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