PPT - Limits & Continuity - 1

PPT - Limits & Continuity - 1 | Quantitative Aptitude for CA Foundation PDF Download

``` 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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Quantitative Aptitude for CA Foundation

147 videos|175 docs|99 tests

FAQs on PPT - Limits & Continuity - 1 - Quantitative Aptitude for CA Foundation

 1. What is the definition of a limit in calculus?
Ans. In calculus, a limit is a fundamental concept that describes the behavior of a function as the input approaches a certain value. It is denoted by the symbol "lim" and is used to determine the value that a function approaches or tends to as the input gets arbitrarily close to a specified value.
 2. How do you evaluate the limit of a function?
Ans. To evaluate the limit of a function, you can use various techniques such as direct substitution, factoring, rationalizing, and trigonometric identities. Additionally, you can apply L'Hopital's rule, which allows you to differentiate the numerator and denominator separately when evaluating certain indeterminate forms.
 3. What is meant by continuity of a function?
Ans. Continuity of a function refers to the absence of any abrupt changes, jumps, or breaks in the graph of the function. A function is said to be continuous if its graph can be drawn without lifting the pen from the paper. This means that there are no holes, vertical asymptotes, or sharp corners in the graph.
 4. How do you determine if a function is continuous at a point?
Ans. To determine if a function is continuous at a specific point, you need to ensure three conditions are met: 1) The function is defined at that point, 2) The limit of the function as it approaches that point exists, and 3) The limit is equal to the value of the function at that point. If all these conditions are satisfied, the function is continuous at that point.
 5. Can a function be continuous but not differentiable?
Ans. Yes, it is possible for a function to be continuous but not differentiable at certain points. This occurs when the function has a sharp corner, a vertical tangent, or a cusp. In such cases, although the function is continuous, its derivative does not exist at those specific points.

Quantitative Aptitude for CA Foundation

147 videos|175 docs|99 tests

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