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

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

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

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{4}

\frac{d}{d x} (A e^{3 x} + 3 A x e^{3 x})

x \to 1 lim (4 x^{5} - 2 x^{4} - 3)

(2, 4), (- 1, - 5)

- 3 y^{^{'}} + \frac{4 y}{x} = \frac{y ^{4}}{x ^{2}}

\frac{\partial}{\partial x} (x cos (y - x))

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