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

### Chapter: 9. Continuity

#### Subject: Maths - Class 12th

##### Q. No. 42 of Exercise 9.1

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

42
##### For what value of is the function continuous at x = 0? What about continuity at x = ± 1?

we have to find the value of '' such that f(x) is continuous at x = 0

If f(x) is be continuous at x = 0,then, f(0)=f(0) + =f(0)

LHL = f(0)=

(02 + 2×0)

0 ...(1)

RHL = f(0) + =

4(0) + 1

1 ...(2)

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

Hence f(x) is not continuous at x = 0

we also have to find out the continuity at point

For f(x) is be continuous at x = 1,

then ,f(0)=f(0) + =f(0)

LHL = f(1) + =

(02–1)

...(1)

RHL = f(1) + =

(5 + 4×0)

5 ...(2)

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

i.e, – = 5

= –5

Hence f(x) is continuous at x = 1,when = –5

Similarly, For f(x) is be continuous at x = –1,

then ,f(–1)=f(–1) + =f(–1)

LHL = f(–1)=

(02 + 4×0 + 3)

–3 ...(3)

RHL = f(–1) + =

(–3 + 4×0)

–3 ...(2)

From (1) & (2),we get, f(–1)=f(–1) +

i.e, –3 = –3

= 1

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