How do you evaluate #(1-cos2x)/(x^2)# as x approaches 0?
If we try to substitute 0 into
When direct substitution yields an indeterminate form, we can use L'Hôpital's rule:
Note that this is not the same as the Product Rule; rather, it means that the limit of the derivative of
Let's try this:
What happens when we substitute 0 back into this?
We end up with
When we substitute 0 into this, we get
This gives if
Thus, we know that
For more on L’Hôpital's rule, I encourage you to check out this link .
# = lim_(xrarr0)(2sin^2x)/x^2#
# = 2 (lim_(xrarr0)(sinx)/x)^2#
# = 2(1)^2 = 2#