# It's a form of a something similar

Calculus Level 4

The limit

$\large \lim_{x \to 3} \left [ \frac{1}{(9-x^2)^{2}} \left( \frac{9+x^2}{3x} - 2\sin \frac{3π}{2} \sin \frac{πx}{2} \right) \right ]$

can be expressed as $$\displaystyle \frac{a + b \pi^ c}{d^a}$$ for positive integers $$a,b,c$$ and $$d.$$ What is the value of $$a+b+c+d?$$

×