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

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

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

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

m

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( m x ) m}{1})

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

Plug in the value

x = 0

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

Simplify

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

= m

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\frac{\partial}{\partial x} (ln (4 x^{2}))

\frac{d ^{2}}{d x ^{2}} (e^{x} sin (x))

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