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Module 7 : Applications of Integration - I

Lecture 21 : Relative rate of growth of functions [Section 21.1]

(iv)
(a)
(v)

2.	Prove the following:
(i)	For any two positive real numbers the function grows slower that as .
(ii)	For any two natural numbers with the function grows slower than as .
(iii)	For any two real number the function grows faster than as .
(iv)	For any real number and the function grows faster than as .
(v)	For any real numbers and the function grows faster than as .

3.	Using exercise(1) arrange the following functions in the descending rate of growth, that is, from the fastest
	growing to the slowest growing, as :


4.	Let be functions such that grow faster than as . Prove that the functions
	grow at the same rate as .

5.	Let is fixed let
	Show that, as grows slower than but grows faster than .