Manipal MET2015MathematicsContinuity and Differentiability

If f(x)= cases ( x)- x ( -2 x)^3 , & x 2 k, & x= 2 cases is a continuous at x= 2 , then k is equal to

Options

A0
B- 1 6
C- 1 24
D- 1 48

Correct answer

D. - 1 48

Step-by-step solution

It is given that f(x) is continuous at x= 2 . k= _ x / 2 f(x) aligned & k= _ x / 2 ( x)- x ( -2 x)^3 & k= _ x / 2 ( x)- x ^3 x ^3 ( 2 -x ) 8 ( 2 -x )^3 & k=- 1 6 1 8 =- 1 48 [ _ x 0 x-x x^3 =- 1 6 ] aligned

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