BBA I Business Maths Limit

1.  LIMIT & DIFFERENTIATION
 Course: BBA
 Subject: Business Mathematics
 Unit-3
1

2. Meaning of Limit:
 Limits are the core tool that we build upon for calculus.
 Many times, a function can be undefined at a point, but we
can think about what the function "approaches" as it gets
closer and closer to that point (this is the "limit").
 Other times, the function may be defined at a point, but it
may approach a different limit.
 There are many, many times where the function value is the
same as the limit at a point.
 Either way, this is a powerful tool as we start thinking about
slope of a tangent line to a curve.

3. Meaning of x → a:
 If a variable x takes increasing or decreasing values all
approximately to a but x does not equal a, we say that x
tends to a.
 Symbolically write x → a.

4. Meaning of x → 0
 When a variable x approaches 0 by taking decreasing
positive values or increasing negative values but x does
not become 0, then we say that x tends to 0 and write x →
0.

5. Meaning of x →∞
 When a variable x takes larger and larger values such that
value of x is greater than a large positive number N, then
we say that x tends to infinity and write x →∞ .

6. Definition: Limit
 Suppose f(x) is a function of real variable x.
 If the function f(x) approaches closer and closer to a fixed
value ‘l’, when the variable ‘x’ approaches closer and
closer to a fixed value ‘a’, then we say that when x tends
to ‘a’, f(x) tends to ‘l’.
 Symbolically, when x → a , f(x) → l.
 lim x → a f(x) = l

7. Properties of limit
Assume that and exist and
that c is any constant. Then,
2.

9. Important formula for limits:
(1)
(2)
(3)
(4)
1
lim
n n
n
x a
x a
na
x a





0
1
lim log
x
e
x
a
a
x


1
lim 1
n
n
e
n
 
  
 
 
1
0
lim 1 m
m
m e

 

10. References:
1.http://www.google.co.in/imgres?imgurl=http%3A%2F%2Fupload.wikimedia.or
g%2Fwikipedia%2Fcommons%2Fthumb%2Fd%2Fd1%2FL%2525C3%2525A
Dmite_01.svg%2F200pxL%2525C3%2525ADmite_01.svg.png&imgrefurl=htt
p%3A%2F%2Fen.wikipedia.org%2Fwiki%2FLimit_(mathematics)&h=200&w
=200&tbnid=6YxWzZVkWNdz8M%3A&zoom=1&docid=Jy9VKYcvWkGua
M&hl=en&ei=GZejVJ2_K4qPuAT97IGQCg&tbm=isch&ved=0CCQQMygB
MAE&iact=rc&uact=3&dur=719&page=1&start=0&ndsp=12
2.https://encryptedtbn1.gstatic.com/images?q=tbn:ANd9GcSWefMU7mafmaDXY
TYeX8N7qRbHq7KSC_6DhMip_i-hlhICbnjY