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

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

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

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

1

Solution steps

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

x - 4

is negative when

x \to 4 -

. Therefore

∣ x - 4 ∣ = - x + 4

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

Simplify

= x \to 4 - lim (1)

x \to a lim c = c

= 1

x \to - \infty lim (- 2 x^{2})

x \to 1 lim (\frac{1}{1 - e ^{\frac{x}{x - 1}}})

x \to 5 lim (\frac{8}{x - 5})

x \to - 1 lim (\frac{x}{x ^{2} - x})

x \to 0 lim (sec^{2} (x) - 1)

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