HSC Arts 12th Board ExamMaharashtra State Board
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Examine the continuity of the following function at given point: f(x)=(logx-log8)/(x-8) ,=8, - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

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

  Is there an error in this question or solution?

APPEARS IN

 2013-2014 (October) (with solutions)
Question 5.1.1 | 3.00 marks
Solution Examine the continuity of the following function at given point: f(x)=(logx-log8)/(x-8) ,=8, Concept: Continuity - Discontinuity of a Function.
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