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

The limit as x approaches 0 of (sin(x/4))/x is 1/4

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

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( \frac{x}{4} ) \frac{1}{4}}{1})

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{4}

\int cos^{3} (x) tan^{2} (x) d x

f (x) = \frac{4}{1 + x ^{2}}, at x = 1

x \to \frac{π}{2} - lim (e^{s e c (x)})

\int \frac{e t}{t} d t

What is the limit as x approaches 0 of (sin(x/4))/x ?
The limit as x approaches 0 of (sin(x/4))/x is 1/4