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Differential Calculus Guide

This document provides an introduction and overview of key concepts in differential calculus, including differentiation and the derivative, limits and continuity, tangents and normals, maxima and minima, and rates of change. It defines differentiation as the algebraic method to find a function's derivative at a point and notes that the derivative represents the rate of change of the y-axis with respect to the x-axis. Continuity and limits are also introduced.

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108 views10 pages

Differential Calculus Guide

This document provides an introduction and overview of key concepts in differential calculus, including differentiation and the derivative, limits and continuity, tangents and normals, maxima and minima, and rates of change. It defines differentiation as the algebraic method to find a function's derivative at a point and notes that the derivative represents the rate of change of the y-axis with respect to the x-axis. Continuity and limits are also introduced.

Uploaded by

sampritc
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Differential

By-Shubham calculus
BCA 2C
A1004816146
TO:-MR. PREAM KUMAR
Index
 Introduction
Differentiation and the Derivative
 Limitand continuity
 Tangent and normal
 Maxima and minima
 Rate
Introduction
Differential calculus is the study of rates of
change of functions, using the tools
of limits and derivatives.
Differentiation and the
Derivative
Differentiation is the algebraic method of
finding the derivative for a function at any point
The derivative of a function is rate of change
of Y axis with X(or slop at a point)
Limit
In mathematics, a limit is the value that a
function "approaches" as the input or index
approaches some value
Continuity
A function is then continuous if it has no holes
or jumps: that is, if it is continuous at every point
of its domain
Tangent and normal
 A straight line or plane that touches a curve or
curved surface at a point, but if extended
does not cross it at that point
Let f(x) is function
Differentiate it m=f’(x) where m is slope
Put value of x( say a)
Find tangent eqn by y-y1 =m(x-x1)
And normal by y-y1 =-1/m(x-x1)
Maxima and minima
 Places where they reach a minimum or
maximum value.
It may not be the minimum or maximum for
the whole function, but locally it is.
Rate
 Rate or speed of change of function

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