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

The limit as x approaches-2 of (sin(|x|))/x is -1/2 sin(2)

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

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

- \frac{1}{2} sin (2)

Decimal Notation

- 0.45464 \dots

Solution steps

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

Plug in the value

x = - 2

= \frac{sin ( ∣ ( - 2 ) ∣ )}{- 2}

Simplify

\frac{sin ( ∣ - 2 ∣ )}{- 2} : - \frac{1}{2} sin (2)

= - \frac{1}{2} sin (2)

x \to 0 lim (tan (x) + \frac{π}{2})

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

x \to 0 - lim (3 (\frac{1}{x} - csc (x)))

x \to 1 lim (\frac{5 x - 5}{x - 1})

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

What is the limit as x approaches-2 of (sin(|x|))/x ?
The limit as x approaches-2 of (sin(|x|))/x is -1/2 sin(2)