What is the limit as x approaches 0 of (sin(16x))/(3x) ?

The limit as x approaches 0 of (sin(16x))/(3x) is 16/3

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limit as x approaches 0 of (sin(16x))/(3x)

x \to 0 lim (\frac{sin ( 16 x )}{3 x})

\frac{16}{3}

Decimal Notation

5.33333 \dots

Solution steps

x \to 0 lim (\frac{sin ( 16 x )}{3 x})

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

= \frac{1}{3} \cdot x \to 0 lim (\frac{sin ( 16 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 16 x ) \cdot 16}{1})

= \frac{1}{3} \cdot x \to 0 lim (\frac{cos ( 16 x ) \cdot 16}{1})

Plug in the value

x = 0

= \frac{1}{3} \cdot \frac{cos ( 16 \cdot 0 ) \cdot 16}{1}

Simplify

\frac{1}{3} \cdot \frac{cos ( 16 \cdot 0 ) \cdot 16}{1} : \frac{16}{3}

= \frac{16}{3}

\int 3^{2 x} d x

\frac{d}{d x} (2, x)

x \to 0 lim (\frac{x - 7}{3 x + 4})

- 9 y^{^{''}} + 36 y = 0

\int 2 y + 1 d y

What is the limit as x approaches 0 of (sin(16x))/(3x) ?
The limit as x approaches 0 of (sin(16x))/(3x) is 16/3