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Example 6  Evaluate

Solution :  Let

L =

=

Here n = 10 and a = 2. Using above formula,

L = 10 (2)10-1 ´

L = 10.29 ´

L = 10 ´ 29-2 = 10 ´ 27 = 10 ´ 128 = 1280

Example 7  Evaluate

Solution : Let L =   form when x = a

\ L   =

Dividing by (x-a) ¹ 0 to both numerator and denominator, we get

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Example 8  Evaluate

Solution :   Let L =

Now n = 1 + 1 + 1 + .......... n times.

Note :

Indeterminate Form : An expression of either of the form , , 0, ¥, 1¥, ¥ - ¥ etc.

The term indeterminate has become obsolete but it has relevance only when certain expressions fall in any of the categories and they cannot be evaluated directly. These are generally obtained by L' Hospital's rule. (Read L'Hospital's rule as Lapital's rule).

Index

Chapter 3