PPT - Limits & Continuity - 1

 Page 1


Limits and Continuity – Intuitive 
Approach  Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Page 2


Limits and Continuity – Intuitive 
Approach  Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Introduction to Function 
• Fundamental Knowledge  
• Its application 
2 
Page 3


Limits and Continuity – Intuitive 
Approach  Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Introduction to Function 
• Fundamental Knowledge  
• Its application 
2 
Definition of Function  
A function is a term used to define relation between 
variables.  
A variable  y is called a function of a variable x if 
for every value of x there is a definite value of y.    
Symbolically y = f(x) 
We can assign values of x arbitrarily. So x is called 
independent variable whereas y is called the dependent 
variable as its values depend upon the value of x. 
3 
Page 4


Limits and Continuity – Intuitive 
Approach  Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Introduction to Function 
• Fundamental Knowledge  
• Its application 
2 
Definition of Function  
A function is a term used to define relation between 
variables.  
A variable  y is called a function of a variable x if 
for every value of x there is a definite value of y.    
Symbolically y = f(x) 
We can assign values of x arbitrarily. So x is called 
independent variable whereas y is called the dependent 
variable as its values depend upon the value of x. 
3 
Types of Functions 
1. Even Function – A function f(x) is said to be even 
function if 
 f(-x) = f(x) 
e.g. f(x) = 2x
2
 + 4x
4
 
 f(-x)  = 2(-x)
2
 + 4(-x)
4
  
 = 2x
2
 + 4x
4 
= f(x)  
Hence 2x
2
 + 4x
4
 is an even function. 
 
4 
Page 5


Limits and Continuity – Intuitive 
Approach  Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Introduction to Function 
• Fundamental Knowledge  
• Its application 
2 
Definition of Function  
A function is a term used to define relation between 
variables.  
A variable  y is called a function of a variable x if 
for every value of x there is a definite value of y.    
Symbolically y = f(x) 
We can assign values of x arbitrarily. So x is called 
independent variable whereas y is called the dependent 
variable as its values depend upon the value of x. 
3 
Types of Functions 
1. Even Function – A function f(x) is said to be even 
function if 
 f(-x) = f(x) 
e.g. f(x) = 2x
2
 + 4x
4
 
 f(-x)  = 2(-x)
2
 + 4(-x)
4
  
 = 2x
2
 + 4x
4 
= f(x)  
Hence 2x
2
 + 4x
4
 is an even function. 
 
4 
Types of Functions - Continued 
2. Odd Function – A function is said to be odd function if 
 f(-x) = - f(x) 
e.g. f(x) = 3x + 2x
5
 
 f(-x)  = 3(-x) + 2(-x)
5 
 
= -3x - 2 x
5
   
 = - (3x + 2 x
5
) = - f(x)  
Hence 3x + 2 x
5
 is an odd function. 
 
5