Applied Mathematics - ll : Limits | Chapter 01 | Lecture 02 Notes for Polytechnic
Adarsh Academy S - Youtube ( Subscribe )
Applied Mathematics - ll : Limits | Chapter 01 | Lecture 02 Notes For Polytechnic.
Hey Everyone, I will Show you Concept Of Limits , Left Hand Limit & Right hand limit & Concept Of Continuity Of A Function, & Show You Some Examples.
Limits Lecture 02 ( Topics )
- The Concept Of Left Hand Limit & Right Hand limit
- Concept Of Continuity Of A Function .
- Some Examples.
Concept Of Limits :-
Let be a Function,
F(x) = X²
Graph Of Function,
If we interested To determine Slope at A Consider a point (O) which is nearly ( Approaches to ) 0 Distance from Point A
- Hence The Distance Between A & O gives Slope of the function at A .
Coordinate Of Point A = ( X1, Y1 )
Coordinate Of Point O = ( X1+h , Y1+h )
Slope at A = Lim F(x)
x→ a
The Concept Of Left Hand & Right Hand Limit
Left Hand Limit ( L.H.L)
Let's Be select a point which is left side from point A say D
Coordinate Of D = ( X-h, Y-h )
where, h approaches to 0
The Value Of Functions Approaches To left side called Left Hand Limit of Function.
Lim F(x) = Lim F ( x - h )
X → a- h→0
Right Hand Limit ( R.H.L )
Take a Point Right Side from Point A say E.
Coordinate Of E = ( X+h , Y+h )
Where, h approaches to 0
The Value Of Functions Approaches To right side called Right Hand Limit of Function.
Lim F(x) = Lim F ( x + h )
X → a+ h→0
Note :-
Limit Of a Functions exist at any point say c
Then ,
L.H.L = R.H.L at Point c.
The Concept Of Continuity Of A Function
- A Function Which Can Be drawn without lifting the pen is called Continuous Function .
Mathematical Defination
L.H.L = R.H.L = Value Of Function at that point
Example - X² Etc .
Applied Mathematics - 2 Chapter 01 |Lecture 02 | Notes Pdf Click Link
For Lecture 01 Notes : Click
Download Your 2 Semester Books Pdf Theory as well as practical Books Pdf & Also Your Syllabus .
- Download Through Given Below Link ⬇️
Syllabus Link :
Theory Books Links :
Practical Books Links :
- Thanks For Visiting -
Comments
Post a Comment