ALGEBRA - solved problems
The limit of a function
Limits of functions properties
Assume that  exist and that c is any constant. Then,
   
   11.   Squeeze rule
           If   f (x) < g (x) < h (x)  for all x in an open interval that contains a, except possibly at x = a
  and    
  then    
   12.  Composition rule
           If   f (x) is continuous at x = b and  
    then,    
Limits of functions properties use
Limits that are commonly used are written below for easy reference,
By comparing the area of the sector of the arc x with areas of the two right triangles, the smaller triangle with legs sin x and cos x, and the bigger triangle with legs tan x and 1, shown on the right figure, we get
Since the left and the right side of the last inequality tend to the same limit 1, as x tends to 0 then, applying the squeeze rule obtained is
   
the fundamental or basic trigonometric limit. Note that the arc length x is measured in radians.
Further,
since both factors on the right tend to 1, as x tends to 0, then
   
Solved problems contents - A
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