What is the limit as x approaches 0 of (sin(5x))/(sin(1/3 x)) ?

The limit as x approaches 0 of (sin(5x))/(sin(1/3 x)) is 15

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limit as x approaches 0 of (sin(5x))/(sin(1/3 x))

x \to 0 lim (\frac{sin ( 5 x )}{sin ( \frac{1}{3} x )})

15

Solution steps

x \to 0 lim (\frac{sin ( 5 x )}{sin ( \frac{1}{3} x )})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 15

\frac{d}{d x} (x^{3} + x^{2} y + x)

f (x) = x^{4} - 20 x^{2} + 64, at x = 1

\frac{\partial}{\partial x} (- \frac{y}{y ^{2} - x ^{2}})

\int 2 x - 3 d x

f (x) = - x + \frac{7}{x} + 1 at x

What is the limit as x approaches 0 of (sin(5x))/(sin(1/3 x)) ?
The limit as x approaches 0 of (sin(5x))/(sin(1/3 x)) is 15