What is the limit as x approaches infinity of |x-5| ?

The limit as x approaches infinity of |x-5| is infinity

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limit as x approaches infinity of |x-5|

x \to \infty lim (∣ x - 5 ∣)

\infty

Solution steps

x \to \infty lim (∣ x - 5 ∣)

x - 5

is positive when

x \to \infty

. Therefore

∣ x - 5 ∣ = x - 5

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

Apply Infinity Property:

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

n is odd

a = 1, n = 1

= \infty

\frac{\partial}{\partial x} (\frac{1}{x + t + 1})

y^{^{'}} = \frac{2 x}{y + 1}

\frac{d}{d x} (arcsech (x))

\frac{d}{d x} (\frac{1}{a + b \cdot ( \frac{x}{d} ) ^{c}})

\frac{d y}{d t} + 5 y = 80, y (1) = 100

What is the limit as x approaches infinity of |x-5| ?
The limit as x approaches infinity of |x-5| is infinity