What is the limit as x approaches 5+of (|x-5|)/(x-5) ?

The limit as x approaches 5+of (|x-5|)/(x-5) is 1

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limit as x approaches 5+of (|x-5|)/(x-5)

x \to 5 + lim (\frac{∣ x - 5 ∣}{x - 5})

1

Solution steps

x \to 5 + lim (\frac{∣ x - 5 ∣}{x - 5})

x - 5

is positive when

x \to 5 +

. Therefore

∣ x - 5 ∣ = x - 5

= x \to 5 + lim (\frac{x - 5}{x - 5})

Simplify

= x \to 5 + lim (1)

x \to a lim c = c

= 1

\int \frac{1}{2 + 7 x ^{2}} d x

\frac{d}{d x} ((\frac{1}{2})^{x})

y^{^{''}} - 9 y^{^{'}} + 3 y = x e^{x}

\int (x^{3} + x^{2} + 2 x - 3) d x

\frac{d}{d x} ((a x^{2} + b x + c) e^{- \frac{x}{6}})

What is the limit as x approaches 5+of (|x-5|)/(x-5) ?
The limit as x approaches 5+of (|x-5|)/(x-5) is 1