How do you find the limit of # sin(7x)/x# as x approaches 0?
we will use well known limit
you cannot use LHopital on this <<--- the bit i would like someone else to confirm
There are "two" ways to solve this limit. The first way to do is it algebraically, and the second way is to apply L'Hospital's rule (although this is technically incorrect - even though the final answer is the same).
In order to solve this limit, we'd have to use a well-known formula, namely the fact that
Since we have
We can now rewrite our limit in the following way:
If we let
Since we already know what this limit is, we simply substitute:
To apply L'Hospital's rule, we have to make sure it is an indeterminate form such as
Since direct substitution yields
Works, but incorrect:
A more detailed explanation and some more examples on L'Hospital's can be found here.