apologiabiology apologiabiology

11-04-2017
Mathematics

contestada

another easy one
[tex] \lim_{h \to 0} \frac{cos( \frac{\pi}{2}+h )}{h} [/tex] is equal to....
find the limit

show all work

Respuesta :

LammettHash LammettHash

14-04-2017

The limit is equivalent to the value of the derivative of [tex]\cos x[/tex] at [tex]x=\dfrac\pi2[/tex]. (See definition of derivative)

[tex](\cos x)'=-\sin x\implies (\cos x)'\bigg|_{x=\pi/2}=-\sin\dfrac\pi2=-1[/tex]

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