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 October 29th, 2017, 11:51 AM #1 Newbie   Joined: Oct 2017 From: azerbaijan Posts: 6 Thanks: 0 What is the solution for this limit? I've been trying to solve this question for 3 hours now still no result. My teacher doesn't let me use L'Hospitals rule and i don't know any other way to solve this
 October 29th, 2017, 12:10 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,691 Thanks: 1350 note ... $\displaystyle f'(a) = \lim_{h \to 0} \dfrac{f(a+h) - f(a)}{h}$ Thanks from topsquark and v8archie
 October 29th, 2017, 12:11 PM #3 Newbie   Joined: Oct 2017 From: azerbaijan Posts: 6 Thanks: 0 I'm not allowed to use derivative(L'Hospitals rule).
 October 29th, 2017, 12:12 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,692 Thanks: 976 Math Focus: Elementary mathematics and beyond What is the limit definition of the derivative for the function sin(x) at x = pi/6?
October 29th, 2017, 12:16 PM   #5
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Quote:
 Originally Posted by lonelymice I'm not allowed to use derivative(L'Hospitals rule).
the note I gave is not L'Hopital ...

 October 29th, 2017, 12:28 PM #6 Newbie   Joined: Oct 2017 From: azerbaijan Posts: 6 Thanks: 0 The teacher specifically told me not to use derivative or L'Hopitals rule for finding the limit.
 October 29th, 2017, 12:36 PM #7 Senior Member   Joined: Dec 2015 From: Earth Posts: 192 Thanks: 23 Use adition formula at $\displaystyle sin(\pi / 6 +x)$ Thanks from topsquark
 October 29th, 2017, 12:45 PM #8 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,116 Thanks: 2369 Math Focus: Mainly analysis and algebra $\sin{(A+B)} =\sin{(A)}\cos{(B)} + \sin{(B)}\cos{(A)}$ You will also have to use $$\lim_{x \to 0} \frac{\sin{(x)}}{x}=1$$ and $$\lim_{x \to 0} \frac{\cos{(x)}-1}{x}=0$$ Thanks from topsquark
October 29th, 2017, 04:20 PM   #9
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Quote:
 Originally Posted by lonelymice The teacher specifically told me not to use derivative or L'Hopitals rule for finding the limit.
You have misunderstood your teacher. "Using the derivative" as skeeter is suggesting has nothing to do with L'Hospital's rule. I can guarantee you that what your teacher has in mind is exactly what he is telling you to do.

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