First calculus question I've seen haha yay:)
[tex] \lim_{x \to 0} \frac{sin4x}{sin6x} [/tex]
substituting x with zero you get [tex]\frac{0}{0}[/tex] therefore you can apply l'hospital's rule and take the derivative of the numerator and the denominator
[tex]\lim_{x \to 0} \frac{sin4x}{sin6x} = \lim_{x \to 0} \frac{ \frac{d}{dx} sin4x }{ \frac{d}{dx} sin6x} [/tex]
[tex]= \lim_{x \to 0} \frac{4cos4x}{6cos6x} [/tex]
[tex]= \frac{4cos4(0)}{6cos6(0)} [/tex]
[tex]= \frac{2}{3} [/tex]
