1.

For what value of k, the function `f(x) ={:{((x^2-4)/(x-2)", " x ne 2),(" "k", " x=2):},` is continuous at x =2.

Answer» Correct Answer - B
It is given that f(x) is right continous at x=2
`therefore underset(xto2^(+))lim f(x)=f(2) `
`Rightarrow underset(hto0)lim f(2+h)=k `
`Rightarrow underset(hto0)lim {(2+h)^(2)+e^((1)/(2-(2-h)))}^(-1)=k`
`Rightarrow (4+0)^(-1)=k Rightarrow k=(1)/(4)`


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