HSC Commerce 12th Board ExamMaharashtra State Board
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Solution - Examine the Continuity of the Following Function - HSC Commerce 12th Board Exam - Mathematics and Statistics

Question

Examine the continuity of the following function : 

`f(x)=x^2-x+9` , for x ≤ 3

        `=4x+3`          for x > 3`

 

Solution

Given

`f(x)=x^2-x+9 , for x<=3`

` =4x+3        for x>3`

`f(3)=(3)^2-3+9=9-3+9`

`f(3)=15`

`Now lim_(x->3^-)f(x)=lim_(x->3)(x^2-x+9)`

                         ` =(3)^2-(3)+9`

                           =15

`lim_(x->3^-)f(x)=lim_(x->3)(4x+3)`

                        =4(3)+3

                        =15

Thus from the above 

`lim_(x->3^-)f(x)=lim_(x->3)f(x)=15=f(3)`

Hence function is continuous at x=3

Is there an error in this question or solution?

APPEARS IN

 2014-2015 (March) (with solutions)
Question 2.1.2 | 3 marks

Reference Material

Solution for question: Examine the Continuity of the Following Function concept: null - Continuous Function of Point. For the courses HSC Commerce, HSC Commerce (Marketing and Salesmanship)
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