What is the limit as x approaches 0 of sin((3x)/x) ?

The limit as x approaches 0 of sin((3x)/x) is sin(3)

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limit as x approaches 0 of sin((3x)/x)

x \to 0 lim (sin (\frac{3 x}{x}))

sin (3)

Decimal

0.14112 \dots

Solution steps

x \to 0 lim (sin (\frac{3 x}{x}))

Cancel the common factor:

x

= x \to 0 lim (sin (3))

x \to a lim c = c

= sin (3)

x \to 0 lim ((1 + \frac{x}{4})^{\frac{1}{x}})

x \to - 1 lim (x^{3} - 3 x + 2)

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

x \to 0 lim (\frac{1}{arcsin ( x )})

x \to 100 lim ((2 x)^{0})

What is the limit as x approaches 0 of sin((3x)/x) ?
The limit as x approaches 0 of sin((3x)/x) is sin(3)