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

Step-by-step solution

Since f(x) is continuous at x = 2 , f(2) = _ x 2 f(x) . f(2) = _ x 2 ( 5x - 8 8 - 3x )^ 3 2x - 4 As x 2 , the base approaches 1 and the exponent approaches , so this is of the form 1^ . Using the standard limit _ x a [h(x)]^ g(x) = e^ _ x a g(x)[h(x) - 1] for 1^ form: f(2) = e^ _ x 2 3 2x - 4 ( 5x - 8 8 - 3x - 1 ) f(2) = e^ _ x 2 3 2(x - 2) ( 5x - 8 - (8 - 3x) 8 - 3x ) f(2) = e^ _ x 2 3 2(x - 2) ( 8x - 16 8 - 3x ) f(2) = e^ _ x 2 3 2(x - 2) 8(x - 2) 8 - 3x f(2) = e^ _ x 2 12 8 - 3x Substituting x = 2 : f(2) = e^ 12