Let me keep on reading:
...., it is common to abbreviate an expression such as "the function f defined by f(x) = x^2+x" to "the function f(x)=x^2+x".
A function f is a rule that assigns .....
Now I am looking at an example in a book.
'Graph the function f(x)=sinx+0.01cos100x'
Another example in the same book.
'f(x)=(x^2-x-2)/(x-2)
This function is discontinuous at a=2, since f(2) is not defined.'
You are contradicting yourself.
Before you said f(x) is the rule of the function f.
Now you are saying f(x) is the value of the function f at the point 'x'.
A rule cannot be a value.
You don't need to use l'Hospital's Rule. However, it gives you a quick answer if you know how to use it.
The question remains open.
May be get help from wolframalpha.
When you finish with this question, do the following one.