What is the limit as x approaches 3-of (x-3)/(|x-3|) ?

The limit as x approaches 3-of (x-3)/(|x-3|) is -1

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limit as x approaches 3-of (x-3)/(|x-3|)

x \to 3 - lim (\frac{x - 3}{∣ x - 3 ∣})

- 1

Solution steps

x \to 3 - lim (\frac{x - 3}{∣ x - 3 ∣})

x - 3

is negative when

x \to 3 -

. Therefore

∣ x - 3 ∣ = - x + 3

= x \to 3 - lim (\frac{x - 3}{- x + 3})

\frac{x - 3}{- x + 3} = - 1

= x \to 3 - lim (- 1)

x \to a lim c = c

= - 1

(- 7) (0.3)

(2, 0), (- 2.5, 1)

\frac{d}{d x} (- 2 x^{5})

t e^{(- 3 t)} sin (5 t)

\frac{\partial}{\partial y} (y^{2} + x y^{3})

What is the limit as x approaches 3-of (x-3)/(|x-3|) ?
The limit as x approaches 3-of (x-3)/(|x-3|) is -1