If the function f (x)= ( 5 x-8 8-3 x )^ 3 2 x-4 if x 2 . = k if x=2 . is continuous at x=2 , then k =

Step-by-step solution

Given, f (x) is continuous at x=2 array ll & f(2)= _ x 2 (x) & k = _ x 2 ( 5 x-8 8-3 x )^ 3 2 x-4 & Put x-2= h & x=2+ h & As x 2, ~h 0 & k = _ h 0 [ 5(2+ h )-8 8-3(2+ h ) ]^ 3 2(2+ h )-4 & k = _ h 0 [ 10+5 ~h -8 8-6-3 ~h ]^ 3 2 ~h & k = _ h 0 [ 2+5 ~h 2-3 ~h ]^ 3 2 ~h array aligned & = _ h 0 (1+ 5 2 h )^ 3 2 h (1- 3 h 2 )^ 3 2 h & = _ h 0 [ (1+ 5 2 h )^ 2 5 h ]^ 5 2 3 2 _ h 0 [ (1- 3 h 2 )^ -2 3 h ]^ -3 2 3 2 aligned aligned & = e^ 15 4 e^ -9 4 & =e^ 24 4 & =e^6 aligned [ array l h 0, 5 h 2 0, -3 h 2 0 and _ h 0 (1