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 1

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

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

1

Solution steps

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

x + 7

is positive when

x \to - 7 +

. Therefore

∣ x + 7 ∣ = x + 7

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

Simplify

= x \to - 7 + lim (1)

x \to a lim c = c

= 1

x \to 0 lim (x ln (x) - 1)

x \to 0 + lim (\frac{sin ( x )}{x})

x \to 3 lim (2 x + 7)

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

x \to - 1 lim (3 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 1