What is the limit as x approaches 7 of (x-7)/(|x-7|) ?

The limit as x approaches 7 of (x-7)/(|x-7|) is diverges

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limit as x approaches 7 of (x-7)/(|x-7|)

x \to 7 lim (\frac{x - 7}{∣ x - 7 ∣})

diverges

Solution steps

x \to 7 lim (\frac{x - 7}{∣ x - 7 ∣})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 7 + lim (\frac{x - 7}{∣ x - 7 ∣}) = 1

x \to 7 - lim (\frac{x - 7}{∣ x - 7 ∣}) = - 1

= diverges

x \to 0 lim (x^{2} + 3 x + 1)

\frac{d y}{d x} + y^{9} x + 5 y = 0

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

\frac{d}{d θ} (cos^{3} (θ))

2 y d y = \frac{5}{x} d x

What is the limit as x approaches 7 of (x-7)/(|x-7|) ?
The limit as x approaches 7 of (x-7)/(|x-7|) is diverges