Continuity and Discontinuity of Functions

1. CONTINUITY

2. Continuity
A function is said to be continuous at x = a
if there is no interruption in the graph of
f(x) at a. Its graph is unbroken at a, and
there is no hole, jump or gap.

3. Continuity of a function at a point
A function is said to be continuous at a point
x = a if the following three conditions are
satisfied:
1.f(x) is defined, that is, exists, at x = a
2.The limit of f(x) as x approaches a exists
3.The limit of f(x) as x approaches a is
equal to f(a).

4. Example: Discuss the continuity of
f(x) = 2 – x
3
at x = 1.

5. DISCONTINUITY

6. Removable Discontinuity
A function is said to have removable
discontinuity at x =a, if the limit of f(x) as x
approaches a exists, and is not equal to
f(a)

7. )(;)(lim afLLxf
ax
¹=
®

8. Jump Discontinuity
A function is said to have jump
discontinuity at x =a, if the limit of f(x)
as x approaches to a from the right is
not equal to the limit of f(x) as x
approaches to a from the left.

9. )(lim)(lim xfxf
axax
+-
®®
=

10. Infinite Discontinuity
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11. ¥=
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12. Check out the videos in our
class portal blog for more…
www.mathonlinelearning.blogspot.com

13. THANK YOU AND
GOODBYE!
I really had a great time
with you!