## Book: RD Sharma - Mathematics (Volume 1)

### Chapter: 9. Continuity

#### Subject: Maths - Class 12th

##### Q. No. 39 of Exercise 9.1

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39
##### Discuss the continuity of the f(x) at the indicated points :f(x) = |x| + |x – 1| at x = 0, 1.

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

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