JEE Main201815 Apr 2018Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let f(x)= array cc (x-1)^ 1 2-x , & x>1, x 2 k, & x=2 array . The value of k for which f is continuous at x=2 is

Options

Ae⁻²
Be
Ce⁻¹
D1

Correct answer

C. e⁻¹

Step-by-step solution

Since f(x) is continuous at x=2 . aligned & _ x 2 f(x)=f(2) & _ x 2 (x-1)^ 1 2-x =k (1^ form ) & e^ l=k aligned where aligned &l= _ x 2 (x-1-1) 1 2-x = _ x 2 x-2 2-x &= _ x 2 ( x-2 x-2 ) & k=e⁻¹ aligned

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