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

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

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

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

3

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply L'Hopital's Rule

= 3 \cdot x \to 0 lim (\frac{cos ( x )}{1})

Plug in the value

x = 0

= 3 \cdot \frac{cos ( 0 )}{1}

Simplify

3 \cdot \frac{cos ( 0 )}{1} : 3

= 3

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