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Byju's Answer
Standard XII
Mathematics
Theorems for Continuity
Check the con...
Question
Check the continuity of the following function at
′
2
′
f
(
x
)
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
x
2
−
4
2
i
f
0
<
x
<
2
0
i
f
x
=
2
2
−
8
x
−
3
i
f
x
>
2
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Solution
f
(
x
)
=
⎧
⎪ ⎪
⎨
⎪ ⎪
⎩
x
2
−
4
2
,
i
f
0
<
x
<
2
0
i
f
x
=
2
2
−
8
x
3
i
f
x
>
2
⎫
⎪ ⎪
⎬
⎪ ⎪
⎭
⇒
f
(
2
)
=
0
lim
x
→
2
f
(
2
)
=
lim
x
→
2
f
(
2
−
h
)
=
lim
x
→
2
(
2
−
h
)
2
2
−
4
=
lim
x
→
2
h
−
4
+
h
2
−
4
2
lim
x
→
2
k
2
−
4
h
2
=
0
lim
x
→
2
f
(
2
+
)
=
lim
x
→
2
f
(
2
+
h
)
=
lim
x
→
2
2
−
8
(
2
+
h
)
3
=
lim
x
→
2
2
(
8
+
12
h
+
6
h
2
+
h
3
)
(
2
+
h
)
3
lim
x
→
2
16
+
24
h
+
2
h
2
+
2
h
3
−
8
(
2
+
h
)
3
=
2
lim
x
→
2
(
4
+
12
h
+
6
h
2
+
h
3
)
(
2
+
h
)
3
=
∴
f
(
2
−
)
≠
f
(
2
)
It is discontinuous
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Similar questions
Q.
Check the continuity of the following function at
2
.
f
(
x
)
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
1
2
(
x
2
−
4
)
i
f
0
<
x
<
2
0
i
f
x
=
2
2
−
8
x
−
3
i
f
x
>
2
.
Q.
Let a function
f
(
x
)
be defined by
f
(
x
)
=
⎧
⎨
⎩
x
2
−
4
x
−
2
:
x
≠
2
4
:
x
=
2
.
Then check the continuity of the function
f
(
x
)
at
x
=
2
.
Q.
Show that the function
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
3
x
−
2
if
0
<
x
≤
1
2
x
2
−
x
if
1
<
x
≤
2
5
x
−
4
if
x
>
2
is continuous at
x
=
2
Q.
Check the continuity of given function :-
f
(
x
)
=
1
−
sin
x
(
π
2
−
x
)
2
,
f
o
r
x
≠
π
2
=
3
,
f
o
r
x
=
π
2
⎫
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎬
⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎭
at
x
=
π
2
.
Q.
Find the value of k,so that the following function is continuous at x = 2.
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
f
(
x
)
=
x
3
+
x
2
−
16
x
+
20
(
x
−
2
)
2
,
x
≠
2
k
,
x
=
2
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