Class 11 Limit and Continuity

ANUPAM SUWAR ANUPAM SUWAR

LIMIT AND CONTINUITY and
.
Let y=f(x) be a function. Then the limit of f(x) is denoted by
defined as the limiting value L if LHL = RHL = L i.e.

INDETERMINANT FORMS

EVALUATION OF ALGEBRAIC LIMIT

 Factorization
Some useful results:

 Rationalization
 Highest Power Common
 Limit Formula

EVALUATION OF TRIGONOMETRIC LIMIT
 Some Standard Results:

 Prove geometrically that:

Proof:
Let, ABC be a circle of radius r. Let, P be a
moving point in the circle.

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Let, AP be an arc which makes  angle at the centre O.
Let, PQ be a tangent at a point P which meets BA produced at Q.
AP is joined. PR AB is drawn.
From the figure,

--- (i)
Here,

[ + --- (iii) ]
--- (ii) ]
*

[
--- (iv)
From equations (i), (ii), (iii) and (iv), we get

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EVALUATION OF LOGARITHMIC AND EXPONENTIAL LIMIT

()

()
Evaluate :
=
= 8+10+7
=25

=
=3
=28

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()

=4
( )[ ]
()
()
()

= -1
[]

= 27
Alternative method,

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*+

()
()

()
()

()
()

=1 [ ]
√ √
[]
√√ √√
√√

√√

√√

√√

√√

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√√
√

√ √* +

√ √√ √
√ √

√√

√√

If b=1, √√
√√

=0
If b

√√

()

√√ √

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√( )
√√
√
√√
√ []
√
√√
√√

[]

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Evaluate: ]
[

[]

[]

()

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[]
()

[]

[]

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[]

()

()
()
()

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()
()

()

[]

= 1+1
=2

[]

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()

[]
()

() )
(

()

Evaluate:

[ ]

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[]

[ ]
()
)
() (
()

()

(

()

)

[]

[ ]

ANUPAM SUWAR

ANUPAM SUWAR