What are some helpful examples for solving limit problems using the squeeze law?

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SUMMARY

This discussion focuses on solving limit problems using the Squeeze Theorem. Specific examples provided include calculating the limits of sin(4/3x) as x approaches 0, tan(π/x) as x approaches 2 from the left, and arctan(2x) as x approaches 0. The Squeeze Theorem is highlighted as a crucial method for evaluating these limits, with a reference to a resource from UC Davis for further examples.

PREREQUISITES
  • Understanding of the Squeeze Theorem in calculus
  • Familiarity with limit notation and evaluation
  • Basic knowledge of trigonometric functions and their limits
  • Experience with arctangent and its properties
NEXT STEPS
  • Study the Squeeze Theorem in detail with examples
  • Practice solving limits involving trigonometric functions
  • Explore the behavior of arctan near zero
  • Review limit properties and techniques for advanced calculus
USEFUL FOR

Students studying calculus, particularly those focusing on limits and the Squeeze Theorem, as well as educators seeking examples for teaching these concepts.

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Homework Statement



I really need help on these problems. If anyone can show me how to solve these problems, your help would be greatly appreciated. Thanks

1- lim x-> 0 sin(4/3x)

2- lim x-> 2- tan(pi/x)

3- limx->0 arctan(2x)


Homework Equations





The Attempt at a Solution

 
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