Sunday, November 16, 2014

Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 47

Find the limit limxπ/4(1tanxsinxcosx)

limxπ/4(1tanxsinxcosx)=limxπ/4(1sinxcosxsinxcosx)=limxπ/4cosxsinxsinxcosx(1cosx)=limxπ/4\cancel(sinxcosx)\cancel(sinxcosx)(1cosx)=limxπ/41cosx=1cosπ4=122=22(By rationalizing the denominator)=2222=\cancel22\cancel2=2

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