What is the limit as x approaches 0+of-(sin(sqrt(x)))/(2*sqrt(x)) ?

The limit as x approaches 0+of-(sin(sqrt(x)))/(2*sqrt(x)) is -1/2

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limit as x approaches 0+of-(sin(sqrt(x)))/(2*sqrt(x))

x \to 0 + lim (- \frac{sin ( x )}{2 \cdot x})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

x \to 0 + lim (- \frac{sin ( x )}{2 x})

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

= - \frac{1}{2} \cdot x \to 0 + lim (\frac{sin ( x )}{x})

Apply L'Hopital's Rule

: x \to 0 + lim \frac{\frac{c o s ( x )}{2 x}}{\frac{1}{2 x}}

= - \frac{1}{2} \cdot x \to 0 + lim \frac{\frac{c o s ( x )}{2 x}}{\frac{1}{2 x}}

Simplify

\frac{\frac{c o s ( x )}{2 x}}{\frac{1}{2 x}} : cos (x)

= - \frac{1}{2} \cdot x \to 0 + lim (cos (x))

Plug in the value

x = 0

= - \frac{1}{2} cos (0)

Simplify

- \frac{1}{2} cos (0) : - \frac{1}{2}

= - \frac{1}{2}

x \to 1 lim (\frac{x - x ^{4}}{1 - x})

x \to - \infty lim (e^{x} x)

x \to 14 lim (2)

x \to 0 lim (ln (x) x)

What is the limit as x approaches 0+of-(sin(sqrt(x)))/(2*sqrt(x)) ?
The limit as x approaches 0+of-(sin(sqrt(x)))/(2*sqrt(x)) is -1/2