# Examine the continuity of the following function at given point: f(x)=(logx-log8)/(x-8) ,=8, - Mathematics and Statistics

Sum

Examine the continuity of the following function at given point:

f(x)=(logx-log8)/(x-8) ,

 =8,

#### Solution

Given f(8)=8

lim_(x->0)f(x)=lim_(x->0)(logx-log8)/(x-8)

=Put x-8=h " then " x=8+h

x->8,h->8

f(8+h)=lim_(x->0)(log(8+h)-log8)/((8+h)-8)

=lim_(x->0)(log((h+8)/8))/h

=lim_(x->0)1/hlog(h+8)/8

=lim_(x->0)log[((h+8)/8)^(8/h)]^(1/8)

therefore f(x)=[1/8loge]=1/8nef(8)

since lim_(x->8) f(x)ne f(8)  is discontinuous at x =8

Concept: Definition of Continuity - Discontinuity of a Function
Is there an error in this question or solution?