HSC Commerce 12th Board ExamMaharashtra State Board
Share

Books Shortlist

# 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

#### 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

#### Video TutorialsVIEW ALL [2]

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.
S