Find the limit as x approaches negative infinity. lim_(x rarr-oo)(sqrt(4x^(2)-3x))/(4x+5)=

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Find the limit as  x approaches negative infinity.  lim_(x rarr-oo)(sqrt(4x^(2)-3x))/(4x+5)=

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Identify highest power of x: Identify the highest power of x in the numerator and denominator. In the expression (sqrt(4x^(2)-3x))/(4x+5), the highest power of x in the numerator inside the square root is x^2, and the highest power of x in the denominator is x.Divide numerator and denominator: Divide the numerator and the denominator by the highest power of x in the denominator. To simplify the limit, we divide both the numerator and the denominator by x. This gives us the following expression: lim_(x rarr-oo)(sqrt(4x^(2)/x^2 - 3x/x^2))/(4x/x + 5/x)Simplify expression inside the limit: Simplify the expression inside the limit. After dividing by x, we get: lim_(x rarr-oo)(sqrt(4 - 3/x))/(4 + 5/x)Evaluate limit as x approaches negative infinity: Evaluate the limit as x approaches negative infinity. As x approaches negative infinity, the terms -3/x and 5/x approach 0. Therefore, the expression simplifies to: lim_(x rarr-oo)(sqrt(4))/(4)Calculate final value of the limit: Calculate the final value of the limit. The square root of 4 is 2, so the expression becomes: lim_(x rarr-oo)(2)/(4) This simplifies to 1/2.

Find the limit as $x$ approaches negative infinity. $\newline$ $\lim _{x \rightarrow-\infty} \frac{\sqrt{4 x^{2}-3 x}}{4 x+5}=$

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Find the limit as $x$ approaches negative infinity. $\newline$ $\lim _{x \rightarrow-\infty} \frac{\sqrt{4 x^{2}-3 x}}{4 x+5}=$