calculus

Ajit Mishra’s Online Classroom: Differentiability Theorem

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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

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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

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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

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

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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 .
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 .

please write your comments if any .

HAPPY CHRISTMAS TO ALL MY FOLLOWERS .

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

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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

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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

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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        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 .

Please wit your questions and comments if any .