MHT CET202120 Sep 2021Evening ShiftMathematicsContinuity and DifferentiabilityActual

If f(x)= 4^ x- +4^ -x -2 (x- )^2 for , is continuous at x= , then = k for = k =

Options

A2 2
B( 2)^2
C-4( 2)^2
D8( 2)^2

Correct answer

C. -4( 2)^2

Step-by-step solution

f( )= _ x f(x)= _ x 4^ x- +4^ -4 -2 (x- )^2 Put x = + h . As x , h 0 aligned & f ( )= _ h 0 4^ h +4^ - h -1-1 ~h ^2 = _ h 0 (4^ h -1 ) h _ h 0 4^ - h -1 - h (-1) & =( 4)(- 4)=(2 2)(-2 2)=-4( 2)^2 aligned

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