1.

Examine the continuity of the following function at given point : `f(x)=(log x-log 8)/(x-8)", for "x ne 8` `"8 ,for "x=8` `"at , "x=8`

Answer» Given `f(8)=8" …(i)"`
`underset(xrarr8)(lim)f(x)=underset(xrarr8)(lim)(logx-log8)/(x-8)`
Putting `x=8+h,` then `x-8=h` and as `xrarr8, hrarr0.`
`therefore" "underset(xrarr8)(lim)f(x)=underset(hrarr0)(lim)(log(8+h)-log8)/(h)`
`=underset(hrarr0)(lim)(log((8+h)/(8)))/(h)`
`=underset(hrarr0)(lim)(log(1+(h)/(8)))/((h)/(8))xx(1)/(8)`
`=(1)/(8)xx1(because underset(xrarr0)(lim)(log(1+x))/(x)=1)" ...(ii)"`
From equation (i) and (ii),
`underset(xrarr8)(lim)f(x) ne f(8)`
`therefore" f is discontinuous at x = 8."`


Discussion

No Comment Found

Related InterviewSolutions