Evaluate without L'Hospital's rule or Series Expansion:
0/0 is an undetermined limit !!!!!!As the numerator is zero, and the denominator tends to zero... In this case the limit will be zero. But as x is not four, but tends to four, I'm not sure if the above trig. expressions can be used.
Anyway, then you can notice that
So if you let , your limit is actually :
, which is (the difference quotient of the function f) equal to