f (x) = Jim n" (at n) (2+ ;) ... (x+:) n! (x2 + n' ) (2 + 4 )... (202 +1 if r > -1 a(r + 2) : a is a constant if x 0, the equation above holds true. Find 83 + 2y- ty. 71-+00 lim cot (7 V 100n? + n + 1) For integer n, the limit above can be expressed as a cos- (30 ) C Vb - 4V5 - 4130 + 6V/5 4 + V10 - 2V/5 + V15 + v3 where a, b, and c are positive integers with a and b being perfect squares. Find a + b + c. Assume that f (a) is continuous on the interval (-oo, oo) and satisfies that x sin f (x) + cos f (x) = x lim n"(r + n) (r+;) ... (x+:) f (z) = n! (x2 + n?) (x2 + 4 ) ... (x2+ 1 if = > -1 a(x + 2) : a is a constant if x