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

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

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

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

- 1

Solution steps

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

x

is positive when

x \to 3 +

. Therefore

∣ x ∣ = x

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

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

= x \to 3 + lim (- 1)

x \to a lim c = c

= - 1

x \to 1 lim (\frac{1}{( x - 1 ) ^{3}})

x \to 5 - lim (\frac{[ x ] - x}{x - 5})

t \to 1 lim (2 t i - 3 j + e^{t} k)

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

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

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