What is the limit as x approaches 4-of (x-4)/(|x-4|) ?

The limit as x approaches 4-of (x-4)/(|x-4|) is -1

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limit as x approaches 4-of (x-4)/(|x-4|)

x \to 4 - lim (\frac{x - 4}{∣ x - 4 ∣})

- 1

Solution steps

x \to 4 - lim (\frac{x - 4}{∣ x - 4 ∣})

x - 4

is negative when

x \to 4 -

. Therefore

∣ x - 4 ∣ = - x + 4

= x \to 4 - lim (\frac{x - 4}{- x + 4})

\frac{x - 4}{- x + 4} = - 1

= x \to 4 - lim (- 1)

x \to a lim c = c

= - 1

y^{2} + 2 x + 2 x y y^{^{'}} = 0

\frac{d r}{d θ} + r tan (θ) = tan (θ)

\frac{d}{d x} (\frac{sin ( x ^{2} )}{x ^{3}})

2 (sin (t) y^{^{'}} + cos (t) y) = cos (t) sin^{3} (t)

f (x) = e^{x^{4}}

What is the limit as x approaches 4-of (x-4)/(|x-4|) ?
The limit as x approaches 4-of (x-4)/(|x-4|) is -1