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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: 2,656 Thanks: 1327  note ... $\displaystyle f'(a) = \lim_{h \to 0} \dfrac{f(a+h)  f(a)}{h}$ 
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: 7,641 Thanks: 959 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 
Math Team Joined: Jul 2011 From: Texas Posts: 2,656 Thanks: 1327  
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: 175 Thanks: 23 
Use adition formula at $\displaystyle sin(\pi / 6 +x) $

October 29th, 2017, 12:45 PM  #8 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,031 Thanks: 2342 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 $$\lim_{x \to 0} \frac{\cos{(x)}1}{x}=0$$ 
October 29th, 2017, 04:20 PM  #9 
Senior Member Joined: Sep 2016 From: USA Posts: 197 Thanks: 105 Math Focus: Dynamical systems, analytic function theory, numerics  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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