What is the limit as x approaches-infinity of (sqrt(4x^2+5x))/x ?

The limit as x approaches-infinity of (sqrt(4x^2+5x))/x is Does not exist

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limit as x approaches-infinity of (sqrt(4x^2+5x))/x

x \to - \infty lim (\frac{4 x ^{2} + 5 x}{x})

Does not exist

Solution steps

x \to - \infty lim (\frac{4 x ^{2} + 5 x}{x})

Factor out

4 x^{2}

from

4 x^{2} + 5 x : 4 x^{2} (1 + \frac{5 x}{4 x ^{2}})

= x \to - \infty lim \frac{4 x ^{2} ( 1 + \frac{5 x}{4 x ^{2}} )}{x}

Simplify

\frac{4 x ^{2} ( 1 + \frac{5 x}{4 x ^{2}} )}{x} : \frac{x ^{2} 4 x + 5}{x x}

= x \to - \infty lim (\frac{x ^{2} 4 x + 5}{x x})

\frac{x ^{2} 4 x + 5}{x x}

undefined for

x

approaching

- \infty

= Does not exist

x \to 0 lim (2 - 6 x + 4 x^{2})

x \to 3 lim (\frac{x - 1}{x ^{2} + 1})

x \to 0 lim (\frac{4}{sin ( x )})

x \to 0 + lim (\frac{ln ( x )}{x - 1})

x \to - 1 lim (\frac{x ^{2} - 2}{x ^{2} - 5 x - 6})

What is the limit as x approaches-infinity of (sqrt(4x^2+5x))/x ?
The limit as x approaches-infinity of (sqrt(4x^2+5x))/x is Does not exist