What is the limit as x approaches 0 of 4/x sin(x/5) ?

The limit as x approaches 0 of 4/x sin(x/5) is 4/5

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limit as x approaches 0 of 4/x sin(x/5)

x \to 0 lim (\frac{4}{x} sin (\frac{x}{5}))

\frac{4}{5}

Decimal

0.8

Solution steps

x \to 0 lim (\frac{4}{x} sin (\frac{x}{5}))

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

= 4 \cdot x \to 0 lim (\frac{1}{x} sin (\frac{x}{5}))

Simplify

\frac{1}{x} sin (\frac{x}{5}) : \frac{sin ( \frac{x}{5} )}{x}

= 4 \cdot x \to 0 lim (\frac{sin ( \frac{x}{5} )}{x})

Apply L'Hopital's Rule

= 4 \cdot x \to 0 lim (\frac{cos ( \frac{x}{5} ) \frac{1}{5}}{1})

Plug in the value

x = 0

= 4 \cdot \frac{cos ( \frac{0}{5} ) \frac{1}{5}}{1}

Simplify

4 \cdot \frac{cos ( \frac{0}{5} ) \frac{1}{5}}{1} : \frac{4}{5}

= \frac{4}{5}

What is the limit as x approaches 0 of 4/x sin(x/5) ?
The limit as x approaches 0 of 4/x sin(x/5) is 4/5