LIMITS ASSIGNMENT 1

1. is equal to

(a)(b)1(c)0(d)

2.If exists then

(a) Both and must exist (b) not exist but exists

(c) Neither nor exists(d) exist but does not exist

3.

(a)1(b)0(c)(d)

4.True statement for is

(a)Does not exist(b)Lies between 0 and

(c)Lies between and 1(d)Greater than 1

5.

(a)(b)(c)(d)None of these

6.

(a)2(b) 2(c)(d)

7.equals(a)2(b)1(c)1(d)3

8.for(a)No value of n(b)n is any whole number(c)n= 0 only(d)n = 2 only

9.

(a)(b)(c)(d)

10.The value of is equal to

(a)(b)(c)(d)None of these

11.denotes greatest integer less than or equal to x)(a)Has value 1(b)Has value 0(c)Has value 1(d)Does not exist

12.(a)1(b) 1(c)0(d)Does not exist

13. is equal to(a) 0(b)1(c)5(d)None of these

14.The values of a and b such that are

(a)(b)(c)(d)None of these

15.(a)0(b)1(c)18(d)36

16.

(a)0(b)(c)(d)None of these

17.The value of is

(a)(b)0(c)1(d)None of these

18.

(a) (b) (c)(d) None of these

19.If is continuous at , then k equals

(a)(b)(c)(d)

20.If is continuous at x = a,then equals

(a)(b)(c)a(d)2a

21.The point of discontinuity of the function = is

(a)(b)(c)(d)All of these

22.Let . If is continuous at then k =

(a)(b)(c)1(d)0

23.Let the value which should be assigned to f at so that it is continuous everywhere is

(a)(b)2(c)2(d)1

24.The value of so that the function = becomes continuous is equal to

(a)(b)(c)2(d)

25.If , then at is(a)Continuous (b)Left continuous (c)Right continuous(d)None of these

26.If , then false statement is

(a) is discontinuous at x = 0(b) is continuous at

(c) is discontinuous at (d) is continuous at

27.The function is continuous for then the most suitable values of a and b are

(a)(b)(c)(d)None of these

28.If is continuous at,then the value of a will be

(a)(b)(c)(d)

29.The number of points at which the function [.] denotes, the greatest integer function) is not continuous is(a)1(b)2(c)3(d)None of these

30.The function where [x] is the greatest integer function is continuous at if

(a)(b)(c)(d)

Answer key 1-(a)2-(a)3-(d)4-(b)5-(c)

6-(c)7-(c)8-(b)9-(c) 10-(a)

11-(a)12-(d)13-(a)14-(c)15-(c)

16-(c)17-(a)18-(a)19-(a)20-(b)

21-(d)22-(a)23-(d)24-(a)25-(c)

26-(b)27-(c)28-(b)29-(b)30-(b)