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

The limit as x approaches 0 of (|x+1|-|x-1|)/x is 2

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

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

2

Solution steps

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

x + 1

is positive when

x \to 0

. Therefore

∣ x + 1 ∣ = x + 1

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

x - 1

is negative when

x \to 0

. Therefore

∣ x - 1 ∣ = - x + 1

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

\frac{x + 1 - ( - x + 1 )}{x} = 2

= x \to 0 lim (2)

x \to a lim c = c

= 2

n = 1 \sum \infty 8

\frac{\partial}{\partial v} (u^{2} + v^{2})

1 - e^{- 0.4 t}

\int \frac{1}{5 + 2 x} d x

(x^{2} + 1)^{(x + 1)}

What is the limit as x approaches 0 of (|x+1|-|x-1|)/x ?
The limit as x approaches 0 of (|x+1|-|x-1|)/x is 2