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

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

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

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

3

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 3

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

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

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

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

x \to 2 lim (\frac{5}{( x - 2 ) ^{3}})

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