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

### Chapter: 9. Continuity

#### Subject: Maths - Class 12th

##### Q. No. 10 of Exercise 9.1

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

10
##### Discuss the continuity of the following functions at the indicated point(s). at x = 1

In this problem we need to check continuity at x = 1

Given function is

at x = 1 …… Equation 2

we need to check LHL, RHL and value of function at x = 1 (for approaching idea and meaning of continuity refer to Q10(i))

Clearly,

f(1) = 2 [ from equation 2]

LHL =

Since h is positive no which is very close to 0

(h–2) is negative and hence h(h–2) is also negative.

|h(h–2)| = –h(h–2)

LHL =

RHL =

Since h is a positive no which is very close to 0

(h+2) is positive and hence h(h–2) is also positive.

|h(h+2)| = h(h+2)

RHL =

Clearly, LHL ≠ RHL

f(x) is discontinuous at x=1

1
2
3
4
5
6
7
8
9
10
10
10
10
10
10
10
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
36
36
36
36
36
36
36
37
38
39
39
40
41
42
43
44
45
46