Module 7 : Applications of Integration - I
Lecture 19 : Definition of the natural exponential function [Section 9.2]
5.

 Let be a twice differentiable functions with continuous and

 

Find .

   
6.

Show that for any ,

 
   
7.

Let be any real number.

 

Show that
         
Interpret this geometrically as the areas.

   
8.

Let be real numbers with . Prove the following:
(i)
  for every .
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