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

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

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

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

- \frac{1}{2}

Decimal

- 0.70710 \dots

Solution steps

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

Rationalize numerator

\frac{2 - x - 2 + x}{x} : - \frac{2}{- x + 2 + x + 2}

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

Plug in the value

x = 0

= - \frac{2}{- 0 + 2 + 0 + 2}

Simplify

= - \frac{1}{2}

x \to 0 lim (\frac{1}{x ^{2}} + ln (x))

x \to 2 lim ((1 + \frac{1}{x})^{x})

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

x \to \frac{π}{2} lim ((\frac{π}{cos ( x )}) - 2 x tan (x))

x \to \infty lim (\frac{5 ^{x + 1}}{e ^{x}})

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