Limit

A PRESENTAITON

AT

NITTTR, AHMEDABAD

PROF. K.K.POKAR

GOVERNMNET ENGINEERING COLLEGE,BHUJ

[email protected]

LIMIT

OVERVIEW

The concept of a limit is a central idea that distingushes

calculus from algebra and trigoniometry. It is fundamental

to finding the tangent to a curve or the velocity of an

object may be the car,plane,…

LEARNING OUTCOMES

In this presentation We use limits to describe the way a function f

varies. Some functions vary continuously; small changes in x produces

only small changes in f(x). Other functions can have values that jump

or vary erractically. The notion of limit gives a precise way to

distinguish between these behaviors. The geometric application of

using limits to define the tangent to a curve leads at once to the

important concept of derivative of a function.

CONCEPT OF LIMIT

THE LIMIT VALUE DOESN’T DEPEND ON HOW THE FUNCTION IS DEFINED AT A POINT

TWO SIDED LIMITS

TWO SIDED LIMITS• Right hand limit:

• Left hand limit:

• It the above two sided limits exists and they are equal then we say that

The limit: exists.

DEFINITION

GEOMETRICAL MEANING

EXAMPLES OF LIMIT

APPLICATIONS OF LIMIT

DERIVATIVE AS A LIMIT

SLOPE OF THE TANGENT

EXPLODING MYTHS ABOUT TANGENT

APPROXIMATION OF A TANGENT BY SECANT

See :-------------

SLOPE OF TANGENT USING THE SLOPE OF SECANT

DEFINITION: SLOPE, TANGENT LINE