What is the limit as x approaches-2+of (x-|x|)/(x+2) ?

The limit as x approaches-2+of (x-|x|)/(x+2) is Does not exist

limit as x approaches-2+of (x-|x|)/(x+2)

x \to - 2 + lim (\frac{x - ∣ x ∣}{x + 2})

Does not exist

Solution steps

x \to - 2 + lim (\frac{x - ∣ x ∣}{x + 2})

x

is negative when

x \to - 2 +

. Therefore

∣ x ∣ = - x

= x \to - 2 + lim (\frac{x - ( - x )}{x + 2})

Multiply by the conjugate of

x - (- x) : \frac{0}{x + ( - x )}

= x \to - 2 + lim (\frac{\frac{0}{x - x}}{x + 2})

\frac{\frac{0}{x - x}}{x + 2}

undefined for

x

approaching

- 2

from the right

= Does not exist

x \to 2 lim (\frac{x}{x ^{3} - 8})

x \to \frac{π ^{+}}{2} lim (tan (x))

x \to 0 lim (x^{2} \cdot csc^{2} (x))

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

x \to \infty lim (\frac{8 x ^{2} - 3 x}{16 x ^{2} - 1})

What is the limit as x approaches-2+of (x-|x|)/(x+2) ?
The limit as x approaches-2+of (x-|x|)/(x+2) is Does not exist