RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 9. Continuity

Subject: Maths - Class 12th

Q. No. 39 of Exercise 9.1

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

39

Discuss the continuity of the f(x) at the indicated points :

f(x) = |x – 1| + |x + 1| at x = – 1, 1.

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


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


LHL = f(–1) =




|(–2–0)| + |–0|


|–2|


|–x| = |x| = x


2 ...(1)


RHL = f(–1) + =




|(–2 + 0)| + |0|


|–x| = |x| = x


|–2|


2 ...(2)


From (1) & (2),we get f(–1)=f(–1) +


Hence ,f(x) is continuous at x = –1


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


LHL = f(1) =




|–0| + |2–0|


|2|


2 ...(3)


RHL = f(1) + =




|0| + |2 + 0|


|–x| = |x| = x


|2|


2 ...(4)


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


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


Chapter Exercises

More Exercise Questions