What is the limit as x approaches 0 of sin((2x)/x) ?

The limit as x approaches 0 of sin((2x)/x) is sin(2)

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limit as x approaches 0 of sin((2x)/x)

x \to 0 lim (sin (\frac{2 x}{x}))

sin (2)

Decimal Notation

0.90929 \dots

Solution steps

x \to 0 lim (sin (\frac{2 x}{x}))

Cancel the common factor:

x

= x \to 0 lim (sin (2))

x \to a lim c = c

= sin (2)

x \to - \infty lim (e^{x} - 5)

x \to 0 lim (\frac{2}{3 + e ^{\frac{1}{x}}})

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

x \to 0 lim (\frac{4 - 4 cos ( x )}{x ^{2}})

x \to 0 lim (\frac{2 ∣ x ∣}{2 x})

What is the limit as x approaches 0 of sin((2x)/x) ?
The limit as x approaches 0 of sin((2x)/x) is sin(2)