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 2.8 The Exponential Limits If then an is monotonic increasing and bounded, then       and    If we put , then as    Hence and   We know that 'e' is an irrational number and 2 < 3 < 3. Also, we shall assume some results without proof.   and   The term log a on R.H.S. has base 'e' which need not be explicitly written. The students should note that the power of 'a' in the numerator viz 'x' must be repeated in the denominator and it must tend to zero. For this sometimes, the denominator has to be readjusted as follows. .... (Since 4x ® 0 as x ® 0 ) Example 1 Find   Solution : L = = = = = 2 (log 3) (1)      = = log 9 Example 2   Find Solution : L =   = = = = log a - log b = log (a / b) Index 2.1 Modulus 2.2 Inequalities 2.3 Limits Of Functions 2.4 Left Hand And Right Hand Limits 2.5 Theorems On The Algebra Of Limits 2.6 Evaluating Limits 2.7 Limits Of Trigonometric Functions 2.8 The Exponential Limits Chapter 3 Follow @Pinkmonkey_com Your browser does not support the IFRAME tag.