The jump value of the function at the point of the discontinuity of the function `f(x)=(1-k^(1/x))/(1+k^(1/x))`(k>0) (k=1) is:

Options

A. 4
B. 2
C. 3
D. None of these

Answer

B

Explanation

Check at x = 0
`LHL=lim_(x to 0^(-))f(x)=lim_(h to 0)f(0-h)`
`=lim_(h to 0)(1-k^(-1//h))/(1+k^(-1//h))=(1-0)/(1+0) " " ["for " k gt 1]`
`=1`
`and RHL=lim_(x to 0^(+)) f(x)=lim_(h to 0) f(0+h)`
`=lim_(h to 0) (1-k^(1//h))/(1+k^(1//h))=lim_(h to 0)(k^(-1//h)-1)/(k^(-1//h)+1)`
`=(0-1)/(0+1)=-1`
`therefore " Jump"=LHL-RHL=1-(-1)=2`