What is the limit as x approaches infinity of (5x^2-x-6)/(x+1) ?

The limit as x approaches infinity of (5x^2-x-6)/(x+1) is infinity

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limit as x approaches infinity of (5x^2-x-6)/(x+1)

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

\infty

Solution steps

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

Simplify

\frac{5 x ^{2} - x - 6}{x + 1} : 5 x - 6

= x \to \infty lim (5 x - 6)

Apply Infinity Property:

x \to \infty lim (a x^{n} + \dots + b x + c) = \infty, a > 0,

n is odd

a = 5, n = 1

= \infty

n \to \infty lim (\frac{n n - 1}{n ^{2} + 1})

x \to 0 lim (x csc (x) sec (x))

x \to 0 lim ((2 + x)^{3} - 8 x)

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

t \to 0 lim (\frac{e ^{- 7 t} - 1}{t})

What is the limit as x approaches infinity of (5x^2-x-6)/(x+1) ?
The limit as x approaches infinity of (5x^2-x-6)/(x+1) is infinity