text: # 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 .
explanation: The document is a collection of blog post excerpts from "Ajit Mishra’s Online Classroom" that cover various topics in calculus and physics, such as the Differentiability Theorem, Polar Coordinates, Motion of a Particle, Equations of First Order, Equations of Tangent and Normal, and Maxima and Minima. Each excerpt introduces a topic and provides a brief explanation or theorem, often with a link to a more detailed discussion.
  
  The document does not contain a specific question or a question and answer. It is a compilation of educational content.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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 .
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a collection of blog post excerpts from "Ajit Mishra’s Online Classroom" that cover various topics in calculus and physics, such as the Differentiability Theorem, Polar Coordinates, Motion of a Particle, Equations of First Order, Equations of Tangent and Normal, and Maxima and Minima. Each excerpt introduces a topic and provides a brief explanation or theorem, often with a link to a more detailed discussion.
  
  The document does not contain a specific question or a question and answer. It is a compilation of educational content.
  
  Label: no-question