It's a form of a something similar

Calculus Level 4

The limit

limx3[1(9x2)2(9+x23x2sin3π2sinπx2)] \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 a+bπcda \displaystyle \frac{a + b \pi^ c}{d^a} for positive integers a,b,c,a,b,c, and d.d.

What is the value of a+b+c+d?a+b+c+d?

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