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UPSC NDA I 2011 Mathematics Paper
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© examsnet.com
Question : 22
Total: 120
What is the value of
k
for which the following function
f
(
x
)
is continuous for all
x
?
f
(
x
)
=
{
x
3
−
3
x
+
2
(
x
−
1
)
2
for
x
≠
1
k
for
x
=
1.
3
2
1
−
1
Validate
Solution:
Since the given function is continuous so that
f
(
1
+
h
)
=
f
(
1
−
h
)
=
f
(
h
)
Now
f
(
1
+
h
)
=
lt
h
→
1
(
1
+
h
)
3
−
3
(
1
+
h
)
+
2
(
1
+
h
−
1
)
2
⇒
lt
h
→
0
1
+
h
3
+
3
h
2
+
3
h
−
3
−
3
h
+
2
(
h
)
2
∴
f
(
x
)
=
3
.
© examsnet.com
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