Upcoming SlideShare
×

Limmits

1,139 views

Published on

1 Comment
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• helpful slide for my students ,atleast i can save my time and explain more

Are you sure you want to  Yes  No
• Be the first to like this

Views
Total views
1,139
On SlideShare
0
From Embeds
0
Number of Embeds
7
Actions
Shares
0
48
1
Likes
0
Embeds 0
No embeds

No notes for slide

Limmits

1. 1. The number Lis called the limit of the function f(x) as x approaches a, written
2. 2. x x
3. 3. x 0 x
4. 4. lim h x 2 x 1 lim h x 1 x 1 lim h x does not exist x 1
5. 5. ) If f(x) = c ( a constant function), then for any a x a n n ) where n is a positive x a integer
6. 6. ) If f x and gx x a x a exist , then x a x a x a
7. 7. ) If lim f ( x ) and g x x a x a exist , then x a x a x a
8. 8. - If lim f ( x ) exists, then for any x a constant k, lim k f ( x )] k lim f ( x ) x a x a
9. 9. lim f ( x ) gx x a x a f (x ) lim f ( x ) x a lim x a g (x ) lim g ( x ) x a
10. 10. ) If lim f ( x ) exits, and n is a positive x a integer n n x a x a
11. 11. If does not exist, since
12. 12. ) 1 lim p 0 where p > 0 x x 1 lim p 0 where p > 0 x x
13. 13. The limit does not exist
14. 14. If f(x) is a rational function and is the term with greatest power in the numerator and is the term with greatest power in the denominator, then
15. 15. A function f(x) is continuous at a point b if and only if: ) f(x) is defined at x = b ) lim f(x) exist x b ) ) lim f(x) = f(b) x b
16. 16. Show that f(x) = / (x- ) is continuous at x= and discontinuous at x = f( )= / lim x f(x) = / =f( ) At x= the function is not defined.
17. 17. The function is not defined at x=- So it is not continuous at x=- , but the limit exist.
18. 18. A polynomial function is continuous at all points of its domain.
19. 19. Find all points of discontinuity of f(x) = x - x + X + X- X + X - = (x+ ) (x- ). The denominator is zero when x=- or x= x=- Thus the function is discontinuous at x=- and x= only.