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

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

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

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

\infty

Solution steps

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

x \to \infty lim (4 x^{2} - 3 x) = \infty

x \to \infty lim (2 x) = \infty

x \to \infty lim (1) = 1

= \infty + \infty + 1

Simplify

\infty + \infty + 1 : \infty

= \infty

x \to 0 lim (\frac{- x}{x})

x \to - 2 lim (5 x)

x \to 0 lim (\frac{2 ^{a x} - 2}{x})

x \to 0 + lim (x ln (6 x))

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

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