Sponsor Area

Limits And Derivatives

Question

Evaluate $space space space space space limit as straight x rightwards arrow straight pi of fraction numerator sin left parenthesis straight n minus straight pi right parenthesis over denominator straight pi left parenthesis straight pi minus straight x right parenthesis end fraction.$

Solution

space space space space space limit as straight x rightwards arrow straight pi space of fraction numerator sin left parenthesis straight pi minus straight x right parenthesis over denominator straight pi left parenthesis straight pi minus straight x right parenthesis end fraction

space space space space space space space space Put space straight x space equals straight pi plus straight h comma space straight x rightwards arrow straight pi rightwards double arrow straight h rightwards arrow 0

∴ $WiredFaculty$

$space space space space space equals space 1 over straight pi straight x 1 equals 1 over straight pi$