CONSIDER THE FUNCTION F(x) = (radical x^3 - 5x) / (radical x (2x-1)) Now conside

Question

CONSIDER THE FUNCTION

F(x) = (radical x^3 - 5x) / (radical x (2x-1))

Now consider this = [radical x^3 - 5x] / [ (radicalx) (2x-1) ]  is equivalent to  (radical x^3) / (radical x times 2x)   is equivalent to (x^3/2) / (2x^3/2)   

Compute the limit as x approaches infinity .

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Explanation / Answer

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Solve sqrt(5x+1) +2 = 2x

sqrt(5x+1) = 2x - 2,

Squaring both sides: 5x + 1 = 4(x-1)^2 = 4x^2 -8x +4.

Or 4x^2 - 13x + 3 =0,

Factoring: (x-3)(4x -1) = 0,

So,x = 3 or 1/4

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