What is the limit as x approaches infinity of (5x-3)/(sqrt(4x^2+3x-1)) ?

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limit as x approaches infinity of (5x-3)/(sqrt(4x^2+3x-1))

x \to \infty lim (\frac{5 x - 3}{4 x ^{2} + 3 x - 1})

\frac{5}{2}

Decimal

2.5

Solution steps

x \to \infty lim (\frac{5 x - 3}{4 x ^{2} + 3 x - 1})

Expand

\frac{5 x - 3}{4 x ^{2} + 3 x - 1} : \frac{5 x}{4 x ^{2} + 3 x - 1} - \frac{3}{4 x ^{2} + 3 x - 1}

= x \to \infty lim (\frac{5 x}{4 x ^{2} + 3 x - 1} - \frac{3}{4 x ^{2} + 3 x - 1})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (\frac{5 x}{4 x ^{2} + 3 x - 1}) - x \to \infty lim (\frac{3}{4 x ^{2} + 3 x - 1})

x \to \infty lim (\frac{5 x}{4 x ^{2} + 3 x - 1}) = \frac{5}{2}

x \to \infty lim (\frac{3}{4 x ^{2} + 3 x - 1}) = 0

= \frac{5}{2} - 0

Simplify

= \frac{5}{2}

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

t \to 0 lim (\frac{sin ( 1 - cos ( t ) )}{1 - cos ( t )})

x \to 1 lim (2 x - 1)

x \to 0 lim (\frac{( 5 ^{x} - 6 ^{x} )}{x})

x \to - 7 + lim (f (x))

What is the limit as x approaches infinity of (5x-3)/(sqrt(4x^2+3x-1)) ?
The limit as x approaches infinity of (5x-3)/(sqrt(4x^2+3x-1)) is 5/2