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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 27
Total: 72
Find
lim
x→5
 f (x) , where f (x) = |x| - 5
Solution:  
We have, f (x) = |x| - 5
Now,
lim
x→5−
 f (x) =
lim
x→5−
 (|x| - 5) =
lim
x→5−
 (x - 5) [Since |x| = x , for x > 0]
= 5 - 5 = 0
and
lim
x→5+
 f (x) =
lim
x→5+
 (|x| - 5)
lim
x→5+
 (x - 5) = 5 - 5 = 0 [Since |x| = x, for x > 0]
∴
lim
x→5−
 f (x) =
lim
x→5+
 f (x)
Thus
lim
x→5
 f (x) = 0.
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