anonymous
  • anonymous
Calculus question! lim f(θ) where f(θ) = {3cos(2θ ) if θ ≤ π θ→ π+ { (sin(θ/2)) / (θ) if θ>π Can anyone show me a step by step solution how to do this so I know how to do the other ones similar to it? Please and thank you! All I know is that I am supposed to use the (sin(θ/2)) / (θ) if θ>π equation. So what do I do next?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
You want to do the left hand and right hand limits.
anonymous
  • anonymous
How would I do that?
anonymous
  • anonymous
\[ \lim_{\theta\to \pi^+}3\cos(2\theta) = 3\cos(2\pi) = 3 \]

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anonymous
  • anonymous
\[ \lim_{\theta\to \pi^-}\frac{\sin(\theta/2)}{\theta} = \frac{\sin(\pi/2)}{\pi} = \frac 1 \pi \]
anonymous
  • anonymous
\[ \lim_{\theta\to\pi^-}f(\theta) \neq \lim_{\theta\to\pi^+}f(\theta) \]The limit does not exist.
anonymous
  • anonymous
Oh! I see, now it makes sense! Thank you so much! SO because the left and right hand sides are not equal to each other, the limit does not exist?
anonymous
  • anonymous
That is a basic fact about limits.

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