anonymous
  • anonymous
Is the answer 1/4 ? The limit as x approaches pi/2 of (1-sinx) / (1+cos2x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Luigi0210
  • Luigi0210
Is this your question: \[\lim_{x \rightarrow \frac{\pi}{2}}\frac{1-sinx}{1+\cos^2x}\]
anonymous
  • anonymous
Could also be \[\cos 2x\]
anonymous
  • anonymous
the bottom is 1+cos(2x)

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Luigi0210
  • Luigi0210
Have you tried plugging in values?
anonymous
  • anonymous
I tried but it says to use l'Hopital's Rule so I did and I got 1/4 I'm not sure if its right though
Luigi0210
  • Luigi0210
Wouldn't it be -1/4?
Luigi0210
  • Luigi0210
Because the derivative of cos2x is -2sin2x
anonymous
  • anonymous
yeah and then i took the derivative again and got 4cos(pi) because when you plug in pi/2 you get 2pi/2 so the 2's cancel out don't they ?
Luigi0210
  • Luigi0210
When using L'hopitals don't we just take the derivative once?
anonymous
  • anonymous
No we can take it more than once if we have to. Well, at least that's what my teacher told us
Luigi0210
  • Luigi0210
No, it's actually just once.
anonymous
  • anonymous
It is ???
Luigi0210
  • Luigi0210
Wait, nevermind sorry, you were right
Luigi0210
  • Luigi0210
Sorry for wasting your time, but yea your answer is right :)
anonymous
  • anonymous
So is the answer 1/4 or -1/4
Luigi0210
  • Luigi0210
1/4
anonymous
  • anonymous
Okay thank you very much for your help :)
Luigi0210
  • Luigi0210
Yup :)

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