Saturday, November 25, 2017

Find the limits without L'Hôpital:limxto0fracxsinxxtanx=?

Find the limits without L'Hôpital's rule
limx0xsinxxtanx=?


My Try:
limx0sin(πx)sinxtan(π+x)tanx=?limx02sin(π2x)cos(π2)sin(π2x)cos(π+x)cos(x)=limx0(2cosx)(cosx)(cos(π2))cosx=0

but:
limx0xsinxxtanx=1/2

Where is my mistake?

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