MHT CET202020 Oct 2020Evening ShiftMathematicsContinuity and DifferentiabilityActual

If aligned f(x) &= (e^ 3 x -1 ) x^ x² if x 0 &= 60 if x=0, then aligned

Options

Af is continuous at x=0
B_ x 0 f(x)=3
Cf has irremovable discontinuity at x=0
Df has removable discontinuity at x=0

Correct answer

A. f is continuous at x=0

Step-by-step solution

_ x 0 f(x)= _ x 0 (e^ 3 x -1 ) x⁰ x² Dividing numerator and denominator by x² , we get array l = _ x 0 ( e^ 3 x -1 3 x 3 ) ( x 180 )⁰ ( x 180 )^ c ( 180 ) = ( x² x² ) =(3)(1) ( 180 ) = 60 array Hence f(x) is continuous at x=0 .

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