Now this final one, this is dealing with trig identities. And in order to do these, you have to be pretty adept at your trig identities. So if we're saying the limit as, let me do that in a darker color. So if we're saying the limit as x approaches zero of sine of x over sine of two x, well, sine of zero zero, sine of zero zero, you're gonna get zero over zero. Once again, indeterminate form, we fall into this category. And now you might recognize this is going to be equal to the limit as x approaches zero of sine of x. We can rewrite sine of two x as two sine x cosine x.