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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 8
Total: 72
lim
x→3
x4−81
2x2−5x−3
Solution:  
We have,
lim
x→3
x4−81
2x2−5x−3
 (0/0 form) =
lim
x→3
(x2−9)(x2+9)
2x2−6x+x−3
=
lim
x→3
(x−3)(x+3)(x2+9)
[2x(x−3)+1(x−3)]
 =
lim
x→3
(x−3)(x+3)(x2+9)
(2x+1)(x−3)
=
(3+3)(9+9)
(6+1)
 =
6×18
7
 =
108
7
.
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