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}

1500 x + 3000 (4 x + 3)^{- 1} - 1000

\frac{d}{d x} (f (x^{2})) = x^{4}

\frac{d ^{2} y}{d θ ^{2}} + y = 0

\int (x^{2} - 2) (x^{3} - 6 x)^{207} d x

x \to 2 lim (3 x^{2})

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