Question

Lim x ->π/4 Cos 2 x/Cosx-Senx =?

Answer 1

Respuesta:

Explicación paso a paso:

Lim x ->π/4 Cos 2 x/Cosx-Senx =

Evaluas

= $\frac{Cos 2(\frac{\pi }{4}) }{Cos \frac{\pi }{4} - Sen \frac{\pi }{4} }$  = $\frac{Cos (\frac{\pi }{2}) }{Cos \frac{\pi }{4} - Sen \frac{\pi }{4} }$ $= \frac{0}{\frac{\sqrt{2} }{2} - \frac{\sqrt{2} }{2} }$ $= \frac{0}{0}$   IND

Antes de evaluar, simplificar

Sabes que Cos 2x = Cos² x - Sen² x = (Cos x + Sen x)(Cos x - Sen x)

reemplaza en la fracción

$\frac{(Cos x+Sen x)(Cos x-Sen x)}{Cos x - Sen x} = Cos x + Sen x$

Lim x ->π/4 (Cos X + Senx) = Cos $\frac{\pi }{4}$ + Sen $\frac{\pi }{4}$ = $\frac{\sqrt{2} }{2} + \frac{\sqrt{2} }{2}$ $= \sqrt{2}$