# PPT - Limits & Continuity - 1 Notes | Study Business Mathematics and Logical Reasoning & Statistics - CA Foundation

## CA Foundation: PPT - Limits & Continuity - 1 Notes | Study Business Mathematics and Logical Reasoning & Statistics - CA Foundation

The document PPT - Limits & Continuity - 1 Notes | Study Business Mathematics and Logical Reasoning & Statistics - CA Foundation is a part of the CA Foundation Course Business Mathematics and Logical Reasoning & Statistics.
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``` 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
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