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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 7
Total: 72
lim
x→2
3x2−x−10
x2−4
Solution:  
We have,
lim
x→2
3x2−x−10
x2−4
 (0/0 form) =
lim
x→2
[3x2−6x+5x−10]
(x−2)(x+2)
=
lim
x→2
[3x(x−2)+5(x−2)]
(x−2)(x+2)
 =
lim
x→2
(3x+5)(x−2)
(x−2)(x+2)
 =
lim
x→2
3x+5
x+2
=
3(2)+5
2+2
 =
6+5
4
 =
11
4
.
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