5: The expression in the numerator is of the type
∞ − ∞.
The leading term under the
root is n4, so when the root is taken into account, the
first term behaves like n2 when n goes to infinity,
that is, it is of the same order as the second term
"-n2".
In intuitive calculations
the leading terms cancel out
![](gif4/eca4ae2.gif)
so we know that factoring out would not help.
Instead the best bet seems to be getting rid of the square root
algebraically, see the box
"difference of roots".
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Answer