Xi Limits Assignment
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ASSIGNMENT
CLASS XI
LIMITS
Evaluate the following limits(Q. 1-28):
1 3x 1 3x x
1. lim x0
x 5 32 x 2 x 3 8
x0
x 2
x2 4 x 2 3x 2
x0
15. lim
cos ecx cot x x0 x
19. lim
x tan 4 x x 0 1 cos 4 x
23. lim
21. lim
sin 3x 7 x x 0 4 x sin 2 x
22. lim
25. lim (sec x tan x)
26. lim
x 2
29. If lim x 3
x3 2 8 x 4 x 4
1 cos mx x 0 1 cos nx
18. lim
x
x 5 243 x 3 x 2 9
x n 3n 108 and n N , find n. x 3
12. lim
sin 2 x sin 6 x x 0 sin 5 x sin 3 x
16. lim
tan x sin x x0 sin 3 x
20. lim
x0
sin x cos x 4 x 4
1 cos x x tan 2 x tan x sin x x0 x3
x 2 tan 2 x tan x
24. lim
sec 2 x 2 4 tan x 1
28. lim
1 cos 3 x x0 x2
sin x sin a x a xa
27. lim x
x 4 1 x3 k 3 lim , find all values of k . x 1 x0 x k
30. If lim x 0
31. Find the value of k so that lim f ( x) may exist, where x 1
x 3 3x 7 f ( x) 3x k
x x 33. Let f ( x ) x 2
5 x 4 x 1 32. If f ( x) 2 , find lim f ( x). x 1 4 x 3 x x 1
1 x 8. lim 2 3 x 1 x x 2 x 1
11. lim
14. lim
x tan x x 0 1 cos x
17. lim
4. lim
x 1 x 1
7. lim
1 2 2 x 3 1 cos x 9. lim 3 10. lim 2 x 2 x 2 x 0 x 3x 2 x x2
13. lim
x2 4x 3 x 3 x 2 2 x 3
3. lim
2 x 2 x x
6. lim
5. lim
x3 8 x 2 x 2
(2 x 3) ( x 1) x 1 2x2 x 3
2. lim
x0
x 1 x 1
.
, show that lim f ( x) does not exist. x 0
x0
ANSWERS 1. 3
2.
1 10
3. 12
4.
1 2
5.
20 3
1 2
10.
1 2
11. 3
12.
135 2
13. 8
17. 2
18.
1 2
19.
1 2
20.
1 2
21.
25. 0
26.
9.
2
27. 2
28. cos a
Downloaded from www.amitbajajmaths.blogspot.com
5 3
29. 4
6.
1 2
7. 2
8.
1 9
14.
m2 n2
15. 4
16.
1 2
22.
1 2
23. 2
24.
9 2
30. 2
3
31. 12
32. 1
CLASS XI
LIMITS
Evaluate the following limits(Q. 1-28):
1 3x 1 3x x
1. lim x0
x 5 32 x 2 x 3 8
x0
x 2
x2 4 x 2 3x 2
x0
15. lim
cos ecx cot x x0 x
19. lim
x tan 4 x x 0 1 cos 4 x
23. lim
21. lim
sin 3x 7 x x 0 4 x sin 2 x
22. lim
25. lim (sec x tan x)
26. lim
x 2
29. If lim x 3
x3 2 8 x 4 x 4
1 cos mx x 0 1 cos nx
18. lim
x
x 5 243 x 3 x 2 9
x n 3n 108 and n N , find n. x 3
12. lim
sin 2 x sin 6 x x 0 sin 5 x sin 3 x
16. lim
tan x sin x x0 sin 3 x
20. lim
x0
sin x cos x 4 x 4
1 cos x x tan 2 x tan x sin x x0 x3
x 2 tan 2 x tan x
24. lim
sec 2 x 2 4 tan x 1
28. lim
1 cos 3 x x0 x2
sin x sin a x a xa
27. lim x
x 4 1 x3 k 3 lim , find all values of k . x 1 x0 x k
30. If lim x 0
31. Find the value of k so that lim f ( x) may exist, where x 1
x 3 3x 7 f ( x) 3x k
x x 33. Let f ( x ) x 2
5 x 4 x 1 32. If f ( x) 2 , find lim f ( x). x 1 4 x 3 x x 1
1 x 8. lim 2 3 x 1 x x 2 x 1
11. lim
14. lim
x tan x x 0 1 cos x
17. lim
4. lim
x 1 x 1
7. lim
1 2 2 x 3 1 cos x 9. lim 3 10. lim 2 x 2 x 2 x 0 x 3x 2 x x2
13. lim
x2 4x 3 x 3 x 2 2 x 3
3. lim
2 x 2 x x
6. lim
5. lim
x3 8 x 2 x 2
(2 x 3) ( x 1) x 1 2x2 x 3
2. lim
x0
x 1 x 1
.
, show that lim f ( x) does not exist. x 0
x0
ANSWERS 1. 3
2.
1 10
3. 12
4.
1 2
5.
20 3
1 2
10.
1 2
11. 3
12.
135 2
13. 8
17. 2
18.
1 2
19.
1 2
20.
1 2
21.
25. 0
26.
9.
2
27. 2
28. cos a
Downloaded from www.amitbajajmaths.blogspot.com
5 3
29. 4
6.
1 2
7. 2
8.
1 9
14.
m2 n2
15. 4
16.
1 2
22.
1 2
23. 2
24.
9 2
30. 2
3
31. 12
32. 1
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