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Transcript of Limit
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A PRESENTAITON
AT
NITTTR, AHMEDABAD
PROF. K.K.POKAR
GOVERNMNET ENGINEERING COLLEGE,BHUJ
LIMIT
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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,…
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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.
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CONCEPT OF LIMIT
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THE LIMIT VALUE DOESN’T DEPEND ON HOW THE FUNCTION IS DEFINED AT A POINT
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TWO SIDED LIMITS
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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.
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DEFINITION
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GEOMETRICAL MEANING
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EXAMPLES OF LIMIT
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APPLICATIONS OF LIMIT
DERIVATIVE AS A LIMIT
SLOPE OF THE TANGENT
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EXPLODING MYTHS ABOUT TANGENT
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APPROXIMATION OF A TANGENT BY SECANT
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See :-------------
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SLOPE OF TANGENT USING THE SLOPE OF SECANT
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DEFINITION: SLOPE, TANGENT LINE