Problems on Limits

Find the limit of the following:

1-

2-

3-

4-

5-

6-

7-

8-

9-

10-

11-

12-

13-

14-

15-

16-

17-

18-

19- Find the value of k where:

Discuss the existence of a limit of the following functions at the given points. Find the limit when it exists.

20-

at x=-1, at x=2

21-

at x=0

22-

at x=0

23-

at x=5,x=0,and x=-3

Problems on continuity

Study the continuity of the functions at the given point:

1-

at x=1,and x=5

2-

at x=3

3-

at x=4

4-

at x=0

5-

at x=0

Rewrite the definition of the following functions to make them continuous at the given points.

6-

at x=-2

7-

at x=0

8- If the function:

is continuous at x=1, and f(1)=7, find a,b.