What is the limit as x approaches infinity of (x^3-4x^2+x+6)/(x+1) ?

The limit as x approaches infinity of (x^3-4x^2+x+6)/(x+1) is infinity

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limit as x approaches infinity of (x^3-4x^2+x+6)/(x+1)

x \to \infty lim (\frac{x ^{3} - 4 x ^{2} + x + 6}{x + 1})

\infty

Solution steps

x \to \infty lim (\frac{x ^{3} - 4 x ^{2} + x + 6}{x + 1})

Simplify

\frac{x ^{3} - 4 x ^{2} + x + 6}{x + 1} : (x - 2) (x - 3)

= x \to \infty lim ((x - 2) (x - 3))

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

With the exception of indeterminate form

= x \to \infty lim (x - 2) \cdot x \to \infty lim (x - 3)

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

x \to \infty lim (x - 3) = \infty

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

\frac{d y}{d x} = x^{2} - 1, y (0) = 1

\int 4 e^{4 x} sin (e^{4 x}) d x

\frac{d}{d x} (\frac{x}{3 x + 1})

\frac{d}{d x} (7 x + x^{2})

\frac{d}{d x} ((2 x^{4} - x + 1) (- x^{5} + 7))

What is the limit as x approaches infinity of (x^3-4x^2+x+6)/(x+1) ?
The limit as x approaches infinity of (x^3-4x^2+x+6)/(x+1) is infinity