1.

Find the value of k so that the function f defined by`f(x)={(kcosx)/(pi-2x),3 , "if" x !=pi/2"if" x=pi/2`is continuous at `x=pi/2`

Answer» Correct Answer - k =6
` f( pi/2-0) = lim_( h to 0) (k cos ( pi /2 -h))/ ( pi -2 ( pi -h)) = lim_( h to 0) ( k sin h )/( 2h) = k / 2 lim_(h to 0) (sin h)/( h ( k/2 xx 1) = k/2`
` f( pi/2 +0) = lim_( h to 0) ( k cos ( pi/2 +h))/( pi-2( pi/2 +h)) = lim_( h to 0) ( - k sin h)/( -2h) = k /2 lim_( h to0) ( sinh )/ h= (k/2 xx 1) = k/2`
` k/2 =3 Rightarrow k=6 `


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