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October 29th, 2017, 11:51 AM   #1
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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

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October 29th, 2017, 12:10 PM   #2
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note ...

$\displaystyle f'(a) = \lim_{h \to 0} \dfrac{f(a+h) - f(a)}{h}$
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October 29th, 2017, 12:11 PM   #3
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I'm not allowed to use derivative(L'Hospitals rule).
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October 29th, 2017, 12:12 PM   #4
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What is the limit definition of the derivative for the function sin(x) at x = pi/6?
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October 29th, 2017, 12:16 PM   #5
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Quote:
Originally Posted by lonelymice View Post
I'm not allowed to use derivative(L'Hospitals rule).
the note I gave is not L'Hopital ...
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October 29th, 2017, 12:28 PM   #6
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The teacher specifically told me not to use derivative or L'Hopitals rule for finding the limit.
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October 29th, 2017, 12:36 PM   #7
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Use adition formula at $\displaystyle sin(\pi / 6 +x) $
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October 29th, 2017, 12:45 PM   #8
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$\sin{(A+B)} =\sin{(A)}\cos{(B)} + \sin{(B)}\cos{(A)}$

You will also have to use $$\lim_{x \to 0} \frac{\sin{(x)}}{x}=1$$ and $$\lim_{x \to 0} \frac{\cos{(x)}-1}{x}=0$$
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October 29th, 2017, 04:20 PM   #9
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Quote:
Originally Posted by lonelymice View Post
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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