Assignment-2 (Maths)---LIMIT AND CONTINUITY

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1. is equal to

a. 1 log_e a

b. 1/2 log_e a

c. a log_e 2

d. none of these

2. is equal to

a. 1

b. ½

c. 1/e

d. 0

3. is

a. ½

b. ¼

c. 0

d. 1

4.

a. 0

b. 2

c. 1

d. ½

5. is equal to

a. 4

b. E

c. 5

d. none of these

6. is

a. n!

b. n-1!

c. –n

d. n

7. equals

a. 0

b. -

c. 2/3

d. None of these

8.

a. Does not exist

b. Is equal to 0

c. is equal to 1

d. exists and different from 0 and 1

9. is equal to

a. 0

b. -1/2

c. ½

d. None of these

10. If f(x)= where [x] denotes the greatest integer x, then equals

a. 1

b. 0

c. -1

d. none of these

11. is equal to

a. 0

b. Ab

c. a-b

d. a+b

12. Let f(x)= , the value of is

a. 0

b. -1/9

c. -1/3

d. 1/9

13. If f(x)= when xa = 1, when x=a then

a. f is continuous everywhere

b. f is continuous at x=a

c. f has limit 1 at x=a

d. limit of x does not exist at x=a

14. The function f(x)=3x-5 for x<3

= x+1 for x>3

=c for x=3. Is continuous at x=3, If c is equal to

a. 1

b. 2

c. 3

d. 4

15. If f(x)=, when x and f( = , then f(x) will be a continuous function at x= when is

a. 1/8

b. ¼

c. ½

d. none of these

16. The function f(x)= if 0

= a if 1

=, if . Is continuous for 0, then the most suitable values for a and b are

a. a=1, b=-1

b. a=-1, b=1+

c. a=-1, b=1

d. none of these

17. f(x)=l= g(x) and f(x) = m = g(x) then the function f(x)-g(x)

a. Is continuous at x=a

b. not continuous at x=a

c. has limit when xàa

d. has a limit equal to l-m when xàa

18. f(x)= sin x, x n, n=0, 1, 2, …….=2, otherwise and g(x)= x² +1, x0,2

= 4, x=0

= 5, x=2, theng(f(x)) is

a. 5

b. 4

c. 2

d. -5

19. The value of is

a. 0

b. 1

c. -1

d. none of these

20. Let f(x)= , x/4. The value which should be assigned to f at x=, so that it is continuous everywhere is

a. 1/2

b. 1

c. 2

d. none of these