# calculus

### Ajit Mishra’s Online Classroom: Differentiability Theorem

Posted on

Theorem :-  A function   f    is differentiable  at     x=a     if and only if there exists a number   l    .
such that ;

f(a+h)-f(a)=lh+hn

Where     n    denotes a quantity which tends to    0     as   h–>0     .

This theorem is known as Differentiability Theorem .

To see the proof of this theorem please click on the given Image or Link .

### Ajit Mishra’s Online Classroom: Polar Co-ordinates

Posted on

This is my another blog post released from my Online Classroom of Mathematics . In this blog post here is a discussion about Polar Co-ordinates an its Unrestricted Verities . Here is also a short Introduction about Transformation of Co-ordinates and Polar Equation of Curves .

To see this Blog Post in detail please Click on the Given Image or Link .

### Ajit Mishra’s Online Classroom: Motion Of A Particle

Posted on

Principles in  the formation of the Equation of Motion of a Particle :-

For Motion in Straight Line ;

Let the mass of the body (particle) be    m    and let the distance of the particle measured from a suitable origin be   x   at the time  t   .

Then acceleration is      (d/dt)(dx/dt)

therefore by Second Law of Motion

m[(d/dt)(dx/dt)] = Forces in the direction of    x   increasing

This is a very important blog post released from my Online Classroom about the equation of motion of a particle which is a very important application of Differential Calculus and useful in Mathematics , Physics , Engineering and Science .
To see this blog post in  detail please click on the given Image or Link

### Ajit Mishra’s Online Classroom: Equations of First Order

Posted on

In this post we will discuss about the equation of first order but not first degree .It is usually denoted

dy/dx    by   p .

Thee are three types of such equations

1) Equations solvable for .
2)Equation solvable for    y  .
3)Equation solvable for    .

This is my another blog post released from my Online Classroom of Mathematics . In which we have discussed about the equation of first order but not first degree . which is very important topic in math and very useful in Physics , Engineering and Science  also .

To see this blog post in details please click on the given Image or Link .

HAPPY CHRISTMAS TO ALL MY FOLLOWERS .

### Ajit Mishra’s Online Classroom: Equations of Tangent and Normal

Posted on

This is my another new blog post released from my Online Classroom of Mathematics in which you will see a short discussion about the equation of tangent and normal .

In this blog post we will discuss in all three type of Cartesian Equation

To see this blog post in details please click on the given Image or Link

### Ajit Mishra’s Online Classroom: Maxima and Minima

Posted on

This is my another blog post released from my Online Classroom of Mathematics . In this post you will see a short discussion about Maxima and Minima , which is :-

Greatest  and Least Value :-

In this section we shall be concerned with the application of Calculus to determining the values of a function which are greatest or least in their immediate neighborhood technically known as  Maximum and Minimum Values .

It will be assumed that    f (x)   possesses continuous derivatives of every order that come in equation .

To see this blog post in details please click to the given Image or Link

### Ajit Mishra’s Online Classroom: Velocity and Acceleration

Posted on

Velocity and Acceleration of a Moving Particles :-

This another blog post released from my Online Classroom of Mathematics . In which we will discuss about Velocity and Acceleration .

If a particle is moving along a straight line , and if at any instant     t     the position        of the particle be given by the distance   s    measured along the path from a suitable fixed point    on it , then      denoting the velocity and   f   the acceleration of the particle at the instant .

To see this blog post in detail please click on the given Image or Link .
The content structure of the provided text is a series of blog post excerpts from "Ajit Mishra’s Online Classroom" that cover various topics in calculus and physics, such as differentiability, polar coordinates, motion of a particle, equations of the first order, equations of tangent and normal, maxima and minima, and velocity and acceleration.
no_question

the text does not contain any mathematical questions or answers to such questions. it is a collection of educational content summaries.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# calculus

### Ajit Mishra’s Online Classroom: Differentiability Theorem

Posted on

Theorem :-  A function   f    is differentiable  at     x=a     if and only if there exists a number   l    .
such that ;

f(a+h)-f(a)=lh+hn

Where     n    denotes a quantity which tends to    0     as   h–>0     .

This theorem is known as Differentiability Theorem .

To see the proof of this theorem please click on the given Image or Link .

### Ajit Mishra’s Online Classroom: Polar Co-ordinates

Posted on

This is my another blog post released from my Online Classroom of Mathematics . In this blog post here is a discussion about Polar Co-ordinates an its Unrestricted Verities . Here is also a short Introduction about Transformation of Co-ordinates and Polar Equation of Curves .

To see this Blog Post in detail please Click on the Given Image or Link .

### Ajit Mishra’s Online Classroom: Motion Of A Particle

Posted on

Principles in  the formation of the Equation of Motion of a Particle :-

For Motion in Straight Line ;

Let the mass of the body (particle) be    m    and let the distance of the particle measured from a suitable origin be   x   at the time  t   .

Then acceleration is      (d/dt)(dx/dt)

therefore by Second Law of Motion

m[(d/dt)(dx/dt)] = Forces in the direction of    x   increasing

This is a very important blog post released from my Online Classroom about the equation of motion of a particle which is a very important application of Differential Calculus and useful in Mathematics , Physics , Engineering and Science .
To see this blog post in  detail please click on the given Image or Link

### Ajit Mishra’s Online Classroom: Equations of First Order

Posted on

In this post we will discuss about the equation of first order but not first degree .It is usually denoted

dy/dx    by   p .

Thee are three types of such equations

1) Equations solvable for .
2)Equation solvable for    y  .
3)Equation solvable for    .

This is my another blog post released from my Online Classroom of Mathematics . In which we have discussed about the equation of first order but not first degree . which is very important topic in math and very useful in Physics , Engineering and Science  also .

To see this blog post in details please click on the given Image or Link .

HAPPY CHRISTMAS TO ALL MY FOLLOWERS .

### Ajit Mishra’s Online Classroom: Equations of Tangent and Normal

Posted on

This is my another new blog post released from my Online Classroom of Mathematics in which you will see a short discussion about the equation of tangent and normal .

In this blog post we will discuss in all three type of Cartesian Equation

To see this blog post in details please click on the given Image or Link

### Ajit Mishra’s Online Classroom: Maxima and Minima

Posted on

This is my another blog post released from my Online Classroom of Mathematics . In this post you will see a short discussion about Maxima and Minima , which is :-

Greatest  and Least Value :-

In this section we shall be concerned with the application of Calculus to determining the values of a function which are greatest or least in their immediate neighborhood technically known as  Maximum and Minimum Values .

It will be assumed that    f (x)   possesses continuous derivatives of every order that come in equation .

To see this blog post in details please click to the given Image or Link

### Ajit Mishra’s Online Classroom: Velocity and Acceleration

Posted on

Velocity and Acceleration of a Moving Particles :-

This another blog post released from my Online Classroom of Mathematics . In which we will discuss about Velocity and Acceleration .

If a particle is moving along a straight line , and if at any instant     t     the position        of the particle be given by the distance   s    measured along the path from a suitable fixed point    on it , then      denoting the velocity and   f   the acceleration of the particle at the instant .

To see this blog post in detail please click on the given Image or Link .
user
The content structure of the provided text is a series of blog post excerpts from "Ajit Mishra’s Online Classroom" that cover various topics in calculus and physics, such as differentiability, polar coordinates, motion of a particle, equations of the first order, equations of tangent and normal, maxima and minima, and velocity and acceleration.

TYPE: NO_QUESTION

The text does not contain any mathematical questions or answers to such questions. It is a collection of educational content summaries.