What is the limit as x approaches 0 of (5sin(3x))/x ?

The limit as x approaches 0 of (5sin(3x))/x is 15

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limit as x approaches 0 of (5sin(3x))/x

x \to 0 lim (\frac{5 sin ( 3 x )}{x})

15

Solution steps

x \to 0 lim (\frac{5 sin ( 3 x )}{x})

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

= 5 \cdot 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})

= 5 \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

Plug in the value

x = 0

= 5 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

5 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : 15

= 15

x \to π lim (π cos (x))

x \to - 1 lim (3 π)

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

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

x \to \infty lim (- x + 7)

What is the limit as x approaches 0 of (5sin(3x))/x ?
The limit as x approaches 0 of (5sin(3x))/x is 15