Evaluate the limit , for is an increasing function and
The Sandwich theorem also known as squeeze play theorem applicable for any three real valued functions and that shares the same domain such that for in the domain of definition states the following:For some real value of , if then
Note that the provide function is an increasing function.The stated limit is
____________(i)
Observe the following for is an increasing function.
As ,, it is evident that
So, the following inequality is of importance
-------------(ii)
Now, divide the inequality (ii) by the function that still preserves the inequality.
--------------(iii)
Apply the squeeze theorem to the inequality (iii) and use the equation (i).
Therefore, the required value of the limit is
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