Use definition as a derivative (as a limit) problem

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SUMMARY

The discussion centers on evaluating the limit of the expression (2cosθ - 1) / (3θ - π) as θ approaches π/3, which results in an indeterminate form of 0/0. Participants clarify that to resolve this, one must apply L'Hôpital's Rule, which involves differentiating the numerator and denominator. Specifically, the derivative of cosθ is -sinθ, which is crucial for simplifying the limit. The problem emphasizes the connection between limits and the definition of derivatives in calculus.

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  • Familiarity with L'Hôpital's Rule
  • Knowledge of trigonometric functions and their derivatives
  • Basic concepts of indeterminate forms
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  • Practice evaluating limits involving trigonometric functions
  • Explore the definition of the derivative and its applications
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Limit → pi/3 [itex]\frac{2cosθ-1}{3θ-pi}[/itex]

I plugged in pi/3 and I got 0/0. I'm not sure that's right way.

Would I need to change the derivative of cosθ to -sinθ? Or just plug pi/3 ?
 
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Could you state the problem exactly as it's given? I'm not seeing how this is related to the definition of the derivative.
 

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