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Solution for Examine the Continuity of F(X)= X 2 − X + 9 for X ⪯ 3 = 4 X + 3 for X > 3 , a T X = 3 - HSC Commerce 12th Board Exam - Mathematics and Statistics

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Question

Examine the continuity of f(x)=`x^2-x+9  "for"  x-<=3`

=`4x+3  "for"  x>3,  at  x=3` 

 

Solution

`f(x)={(x^2,-x,+9, "for"  x,- <=3 ), (4x,+,3 ,"for"  ,x>3):}` 

We check the continuity at x = 3 

LHL (at x=3) 

= `Lim_(x→3-) f(x)` 

=` lim_(h→0) f(3-h)` 

=`Lim_(h→0)[(3-h)^2(3-h)+9]` 

=`Lim_(h→0)[9+h^2-6h-3+h+9]=15` 

`"RHL" (at x=3)=Lim_(x→3_+) f(x)=Lim_(h→0) f(3+h)` 

= `Lim_(h→0) [4(3+h)+3=15]` 

Also      `f(3)=9-3+9=15` 

Hence LHL = `f(3)=RHL` 

Hence f (x) is continuous at x = 3 

  Is there an error in this question or solution?

APPEARS IN

 2017-2018 (March) (with solutions)
Question 1.3 | 2.00 marks
Solution Examine the Continuity of F(X)= X 2 − X + 9 for X ⪯ 3 = 4 X + 3 for X > 3 , a T X = 3 Concept: Continuous Function of Point.
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