# calculus

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

Ajit Mishra’s Online Classroom: Differentiability Theorem.

**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

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

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

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

**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

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

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

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

**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 ** p **.

2)Equation solvable for ** y .**

3)Equation solvable for ** x ** .

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 .**

please write your comments if any .

**HAPPY CHRISTMAS TO ALL MY FOLLOWERS .**

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

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

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 **

please write your comments or questions if any .

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

Ajit Mishra’s Online Classroom: Maxima and Minima.

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**

Please writ your questions or comments if any .

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

Ajit Mishra’s Online Classroom: Velocity and Acceleration.

**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 ** P ** of the particle be given by the distance ** s **measured along the path from a suitable fixed point ** A ** on it , then ** v ** 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 .**

Please wit your questions and comments if any .