Question

Lim x->a xsina-asinx

Answer 1

 

Limit x -> a   x sina - asinx / x - a

 Limit x -> a   xsina - asinx + asina - asina / x - a

Limit x -> a  ( x - a ) sina  / x - a      - a ( sinx - sina ) / x - a

Limit x -> a      sina     -a Limit x -> a  ( sinx - sina ) / x - a                         ( ∴sinc - sind = 2 cos(c+d) / 2  sin(c-d ) /2 )

Limit x -> a   sina   -a Limit x -> a   2cos( x+a) /2 sin( x - a) /2  / x - a

sina         -2acos( a+a) /2  Limit x -> a    sin (x -a )/ 2 / x - a

sina     -2acos( 2a ) /2      Limit x - a /2 -> a - a/2   sin (x -a )/ 2 / x - a /2  x 1/2

sina  -2acosa     1 x 1/2

sina - acosa

 solved ..

hope its help u