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anonymous
 3 years ago
In Problem Set 1: Problem 1J2:
How does d/dx cos(x) when x is PI/2 = Cos(x)Cos(PI/2)/(xPI/2). Shouldn't the numerator be Cos(xPI/2)Cos(PI/2)? (Difference Quotient)
anonymous
 3 years ago
In Problem Set 1: Problem 1J2: How does d/dx cos(x) when x is PI/2 = Cos(x)Cos(PI/2)/(xPI/2). Shouldn't the numerator be Cos(xPI/2)Cos(PI/2)? (Difference Quotient)

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NoelGreco
 3 years ago
Best ResponseYou've already chosen the best response.0Some people who might want to help you may not know how to find problem 1J2. Posting a link might get you more help.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks for the advice. http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/1.differentiation/partadefinitionandbasicrules/problemset1/MIT18_01SC_pset1prb.pdf

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0We define derivative this way: \[ f'(x) = \lim_{\Delta x \rightarrow 0 } \frac { f(x + \Delta x)  f(x) } { \Delta x } \] Substitute \[ \Delta x = x_0  x \] to get \[ f'(x) = \lim_{ x \rightarrow x_0 } \frac { f(x + (x_0  x))  f(x) } { x_0  x } \\ = \lim_{ x \rightarrow x_0 } \frac { f(x_0)  f(x) } { x_0  x } \\ = \lim_{ x \rightarrow x_0 } \frac {  (f(x)  f(x_0)) } { (x  x_0) } \\ = \lim_{ x \rightarrow x_0 } \frac { f(x)  f(x_0) } { x  x_0 } \] Therefore \[ \cos'(x) = \lim_{x \rightarrow \pi/2} \frac { \cos ( x )  \cos (\pi /2) } { x  \pi/2} = \lim_{x \rightarrow \pi/2} \frac { \cos ( x )  \cos( \pi /2) } { x  \pi/2} \]
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