KCET2011MathematicsContinuity and Differentiability

f(x)= array cc x x-1 , & if x 1 k, & if x=1 array . is continuous at x=1 , then the value of k is

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Correct answer

C. 1

Step-by-step solution

Given, f(x)= array cl x x-1 , & if x 1 k & , if x=1 array . at x=1 Since, the function is continuous at x=1 . Then, f(1)= _ x 1 f(x) k= _ x 1 x x-1 ( 0 0 from ) Apply L'hopital rule, aligned &k= _ x 1 1 / x 1 = 1 / 1 1 &k=1 aligned k=1

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