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NDA Math Limit, Continuity and Differentiability
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© examsnet.com
Question : 73
Total: 105
If
f
(
x
)
=
√
25
−
x
2
,then what is
lim
x
→
1
f
(
x
)
−
f
(
1
)
x
−
1
equal to ?
[NDA II 2015]
1
5
1
24
√
24
−
1
√
24
Validate
Solution:
f
(
x
)
=
√
25
−
x
2
f
(
1
)
=
√
24
⇒
lim
x
→
1
f
(
x
)
−
f
(
1
)
x
−
1
∴ It is
0
0
(undefined condition) so using L’hospital’s rule
⇒
lim
x
→
1
f
′
(
x
)
−
0
1
=
lim
x
→
1
(
√
25
−
x
2
)
′
⇒
lim
x
→
1
1
2
×
1
√
25
−
x
2
(
−
2
x
)
=
1
2
×
1
√
25
−
(
1
)
2
×
(
−
2
)
=
−
1
√
24
© examsnet.com
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