CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 13 – Limits and Derivatives Maths
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Question 16:
Evaluate the given limit:
Solution 6:
cos x
lim
x 0 x
= cos0
1
0
cos x
lim
x 0
x
Question 17:
Evaluate the Given limit:
Solution 17:
lim cos2x
1
x0
cos x 1
cos2x
1
lim
x0
cos x 1
At x = 0, the value of the given function takes the form 0 0 .
2
cos2 1
Now, lim x
x0
cos x = lim 12sin x1
cos 1 2sin 2 x
x
1 x0 2 x
1 2sin 1
2
2
2
sin
x 2
2 x
2
sin x
x
lim
lim
x0 2 x x0
sin
2 x
2 sin
2
2 x
2
x
4
2
2
sin
x
lim
x 0
2
x
4
2 x
sin
lim
2
x0
2
x
2
2
2
sin x
lim
x 0
2
x
x
4
x 0 0
2
2
2 x
limsin 2
x0
2
x
2
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