If the function f(x) , defined below, is continuous everywhere, then k equals f(x)= array cc 2^x-1 1+x -1 , & -1 x

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If the function f(x) , defined below, is continuous everywhere, then k equals f(x)= array cc 2^x-1 1+x -1 , & -1 x < k, & x=0 array .

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Correct answer: B. _e 4

Given, f(x)= array ccc 2^x-1 1+x -1 , & -1 x < k, & x=0 array . is continuous everywhere. Since, f(x) is continuous everywhere f(x) will be continuous at x=0 _ x 0 f(x)=f(0) _ x 0 2^x-1 1+x -1 =k [ 0 0 . form, so by applying L^ Hospital rule ] aligned & _ x 0 2^x 2 1 2 1+x =k & _ x 0 2^ x+1 1+x 2=k aligned array ll & 2 1+0 2=k k=2 _e 2 & k= _e 4 array

If the function f(x) , defined below, is continuous everywhere, then k equals f(x)= array cc 2^x-1 1+x -1 , & -1 x < k, & x=0 array .

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