Question: lim n (x +n) (3+; ) ..(x+:) n! (x2 + n?) (x2 + )... (2 2 +1 if x > -1 a(r + 2)

lim n" (x +n) (3+; ) ..(x+:) n! (x2 + n?) (x2 + " )... (2 2 +1 if x > -1 a(r + 2) : a is a constant ifr 0, the equation above holds true. Find y' + 2y- + y. n-+00 lim cot (7 V100n2 + n + 1 For integer n, the limit above can be expressed as a cos- (3) C Vb- 4V5 -4V30 + 6V5 4+ V10 - 2V/5 + \\15 + v3 where a, b, and c are positive integers with a and b being perfect squares. Find a + b + c. Assume that f (x) is continuous on the interval (-oo, co) and satisfies that x sin f (x) + cos f (x) = r

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