Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.9

( 1) 2

=^ + − +^

n L (^)
a n n n h
a a
∴ Lt→ Lt→ 0 ( 1) 2
− = (^) + − +
−^ L^
n n n
x a h
x a a n nn h
x a a a
=a nan⋅n= n−^1
a
Method III. (Rationalisation)
This method is useful where radical sings are involved either in the numerator or denominator. The numerator
or denominator (as required) is rationalized and limit taken. The following example will make the method
clear.
Example 26: Evaluate xLt→ 0 1 +x x−x^1 −
Solution:
Rationalising the numerator, we get
1 1 1 1 1 1
1 1

+ − − = + − + × + + −

+ + −

x x x x x x

x x x x

2

1 1

=

+ + −

x

x x x

2

1 1

=

+x+ −x

∴ 0 0
Lt^11 Lt^21
→ → 1 1

+ − − = =

x x + − −

x x

x x x

Infinite Limits

For finding the limit of

( ) ( )

= ( )

f x g x

h x as a→∝, we divided the numerator and denominator by highest power of

x occurring in f(x) (numerator or denominator whichever power is high) and then use^1 x, x^12 , etc.→0 as
x→∝.
Example 27: Evaluate

Lt ( 1)(2 3)

→∞( 2)(3 4)

+ +

x + +

x x

x x