Hawkeye!

Algebra Level 4

f(x)=x(x1)(2x1)(x2)\large f(x) = \dfrac{ x(x-1)}{(2x-1)(x-2)}

Let the range of the function f(x)f(x) above be (a,b) (a,b) . Find the value of limyb5y2y+3y\displaystyle \lim _{y \to b} \frac{5^y}{2^y +3 ^y} . If you think the limit does not exist, submit your answer as 42.

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