Q. 39 A3.6( 7 Votes )

Discuss the conti

Answer :

To prove whether f(x) is continuous at x = 0 & 1


If f(x) to be continuous at x = 0,we have to show that f(0)=f(0) + = f(0)


LHL = f(0) =




|(–0)| + |(–0)–1|


–|x| = |x| = x


|–1|


1 ...(1)


RHL = f(0) + =




|0| + |0–1|


–|x| = |x| = x


|–1|


1 ...(2)


From (1) & (2),we get f(0)=f(0) +


Hence ,f(x) is continuous at x = 0


If f(x) to be continuous at x = 1,we have to show, f(1) =f(1) + = f(1)


LHL = f(1) =




|(1–0) + (–0)|


|(1)|


1 ...(3)


RHL = f(1) + =




|(1 + 0)| + |0|


–|x| = |x| = x


|1|


1 ...(4)


From (3) & (4),we get f(1) = f(1) +


Hence ,f(x) is continuous at x = 1


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find which of theMathematics - Exemplar

Discuss the contiRD Sharma - Volume 1

Find which of theMathematics - Exemplar

Find which of theMathematics - Exemplar

If <iMathematics - Exemplar

<img width=Mathematics - Exemplar

Find the value ofMathematics - Exemplar

Discuss the contiRD Sharma - Volume 1

Discuss the contiRD Sharma - Volume 1

Find the value ofMathematics - Exemplar