What is the limit as x approaches 0-of (x+1)/(|x|) ?

The limit as x approaches 0-of (x+1)/(|x|) is infinity

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limit as x approaches 0-of (x+1)/(|x|)

x \to 0 - lim (\frac{x + 1}{∣ x ∣})

\infty

Solution steps

x \to 0 - lim (\frac{x + 1}{∣ x ∣})

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

= x \to 0 - lim (\frac{x + 1}{- x})

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

= - x \to 0 - lim (\frac{x + 1}{x})

Divide by highest denominator power:

1 + \frac{1}{x}

= - x \to 0 - lim (1 + \frac{1}{x})

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 0 - lim (1) + x \to 0 - lim (\frac{1}{x}))

x \to 0 - lim (1) = 1

x \to 0 - lim (\frac{1}{x}) = - \infty

= - (1 - \infty)

Simplify

- (1 - \infty) : \infty

= \infty

x \to - 2 lim (\frac{2 x - 3}{x - 4})

x \to - 2 lim (\frac{3 - 5 x}{4 x})

h \to 0 lim (\frac{∣ x h ∣}{h})

x \to 1 lim (I n x)

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

What is the limit as x approaches 0-of (x+1)/(|x|) ?
The limit as x approaches 0-of (x+1)/(|x|) is infinity