ABHAY MAHAJAN
B.Tech. IIT Roorkee
➔ 11+ years teaching experience
➔ Mentored and taught around 20000+ students
➔ Produced 400+ IIT selections
➔ 10+ INMO selections
➔ 1 EGMO Selection
Standard Notation
x → a– This is read as ‘x is approaching to ‘a’ from LHS’
x → a+ This is read as ‘x’ is approaching ‘a’ from RHS’
x → a doesn’t mean x = a
Left Hand Limit
4 3
2
LHS 2 2
Right Hand Limit
4 3
2
2 2
RHS
Limit at a point
Limit of a function at x → a is the value
towards which f(x) approaches when x → a
and it is denoted as
Limit Existence
exists if and only if
= finite
⇓ ⇓
RHL LHL
Concept of LHL, RHL and Limits
(1) (3)
(2) (4)
Understanding Limits
f(x)
1
½
–2 –1 0 1 2 3
Concept of LHL, RHL and Limits
Try to observe
(a) LHL of [x] at x = 3
that is, is ______; here [.] ⟶ GIF
(b) RHL of [x] at x = 3
that is, is ______; here [.] ⟶ GIF
(c) is ______; here [.] ⟶ GIF
(d) is ______; here {.} ⟶ FPF
Q. Evaluate the following using the formula for
RHL & LHL where [.] ⟶ GIF
(a)
Solution
Q. Evaluate the following using the formula for
RHL & LHL where [.] ⟶ GIF
(b)
Solution
Q. Let [.] be GIF, then
A –2
B 1
C –4
D 4
Q. Let [.] be GIF, then
A –2
B 1
C –4
D 4
Solution
Q. For what value of ‘m’ does the
exist if
Solution
Algebra of limits
Let = l and = m.
If l & m are finite, then:
A {f (x) ± g (x)} = l ± m
B {f (x). g (x)} = l.m
C ,provided m ≠ 0
D f(x) = kℓ;
where k is a constant
Q.
Solution
Q. If and
then find the value of
Solution
Indeterminate forms
Consider
Here x2 – 4 = 0 and x–2=0
f(x) has indeterminate form of the type
has indeterminate form of the type
∞
is an indeterminate form of the type 1
Indeterminate forms
As the name suggest; we can’t determine
these values in their present form
There are total 7 Indeterminate Forms
Indeterminate forms
Note:
Here 0 is denoting a function tending to
zero, similarly ∞ & 1 are denoting functions
tending to ∞ & 1 respectively.
is an indeterminate form whereas
is not an indeterminate form.
How to solve the limits
To find first put x = a
If it is determinant finite value then Directly put the
value and
if f (a) is indeterminate form than we have to apply
some method to find the limit.
H L [4+ ] = 4
R
LH
L [4– ] = 3
When their is GIF, Fractional part and function
with multiple function always check RHL & LHL
Direct Substitution
It is used when limit is not in indeterminate form
As the name suggests; we simply put the value
of the variable
Example
Methods for
evaluating
Limits
Methods for evaluating Limits
(a) Factorization Method
Example:
Recall
If x = a is zero of a polynomial P(x)
then x – a must be factor of P(x)
Q. Evaluate the following: (a)
Solution
Q. Evaluate the following: (b)
Solution
Methods for evaluating Limits
(b) Rationalization Method
This is normally used when either
numerator or denominator or both
involve square roots.
Example:
Q. Evaluate the following: (a)
Solution
Q.
D none
Q.
D none
Solution
MASTER CLASS
TEACHER TEACHER
Post-class: doubt solving
More than 2 Million doubts solved
Assessment: regular tests
How to Avail Discount ?
Special Discount for this class
Apply Coupon Code:
AMMPRO
Visit: https://vdnt.in/YTPRO
Link in Description
JEE 2021 Action Plan April Attempt
JEE 2021 Action Plan April Attempt
JEE 2021 8th
Action Plan April
Jan 2020-(Shift 1) Attempt
