I. LIMIT OF FUNCTIONS

1. Find the limit of the following functions as (i) (ii)

(a) (b) (c)

(d) (e) (f)

2. Evaluate

(a) (b)

(c) (d)

(e) (f)

4. (a) Find the limit of as (i) (ii) (iii)

(iv) (v)

(b) Show that and hence find the limit of as (i) (ii) (iii) (iv) (v)

(c) Show that , hence find the value of

(i) (ii) (c)

5. If , write an expression for , and hence evaluate the expression .

6. Evaluate (a) (b) (c)

7. Evaluate if (i) (ii) (iii)

8. Find (a) (b)

9. Differentiate the following function from the first principle:

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

10. Evaluate the following limits:

(a) (b)

(c) (d)

11. Evaluate the following limits:

(a) (b)

(c) (d)

(e) (f)

12. Find the following limits:

(a) (b)

(c) (d)

(e)

13. Evaluate the following limits:

(a) (b)

14. Find the following limits:

(a) (b)

(c) (d)

15. Find the following limits:

(a) (b)

(c)

(d) (e)

16. Find the following limits:

(a) (b)

(c) (d)

17. Find the following limits:

(a) (b)

18. Find the following limits:

(a) (b)

(c) (d)