1. RAYAT SHIKSHAN SANSTHA’S S. M. JOSHI COLLEGE HADAPSAR, PUNE-411028
RAYAT SHIKSHAN SANSTHA’S S.M.JOSHI COLLEGE HADAPSAR, PUNE PRESANTATION TION BY Prof . DESAI S.S Mathematics department Subject – Real analysis Topic Limit of function

2. Limit L a

3. The Definition of Limita

5. Examples
What do we do with the x?

6. 1/2 1
3/2

7. One-Sided Limit One-Sided Limits
The right-hand limit of f (x), as x approaches a, equals L
written:
if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently close to the right of a. L a

8. The left-hand limit of f (x), as x approaches a, equals M
written:
if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently close to the left of a. M a

9. Examples of One-Sided Limit
1. Given
Find
Find

10. A Theorem This theorem is used to show a limit does not exist.
For the function
But

11. Indeterminate Forms
Indeterminate forms occur when substitution in the limit results in 0/0. In such cases either factor or rationalize the expressions.
Notice form
Ex.
Factor and cancel common factors

12. More Examples

13. The Squeezing Theorem
See Graph

14. THANK YOU