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phi
 7 months ago
Best ResponseYou've already chosen the best response.0They are saying it is easy to find the derivative of cos(x) and evaluate it at x= pi/2 \[ \cos'(x)\bigg_{x= \frac{\pi}{2} }= ?\] The other idea is that the expression \[ \lim_{x\rightarrow \frac{\pi}{2} } \frac{\cos(x)}{x\frac{\pi}{2}}\] is vaguely reminiscent of the definition of the derivative \[ f'(x) = \lim_{\Delta\rightarrow 0} \frac{ f(x+\Delta) f(x)}{\Delta}\] Now if you can show that the given expression can be rewritten to look like the definition of the derivative, then you can claim that it and the derivative (evaluated at pi/2) have the same value (1 in this case) I would begin by letting \( x = \frac{\pi}{2} + \Delta \) in the given expression.
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