What is the limit as x approaches 0 of x/(sqrt(5-x)-\sqrt{5+x)} ?

The limit as x approaches 0 of x/(sqrt(5-x)-\sqrt{5+x)} is -sqrt(5)

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limit as x approaches 0 of x/(sqrt(5-x)-\sqrt{5+x)}

x \to 0 lim (\frac{x}{5 - x - 5 + x})

- 5

Decimal Notation

- 2.23606 \dots

Solution steps

x \to 0 lim (\frac{x}{5 - x - 5 + x})

Multiply by the conjugate of

5 - x - 5 + x : \frac{- 2 x}{5 - x + 5 + x}

= x \to 0 lim (\frac{x}{\frac{- 2 x}{5 - x + 5 + x}})

Simplify

\frac{x}{\frac{- 2 x}{5 - x + 5 + x}} : - \frac{1}{2} (- x + 5 + x + 5)

= x \to 0 lim (- \frac{1}{2} (- x + 5 + x + 5))

Plug in the value

x = 0

= - \frac{1}{2} (- 0 + 5 + 0 + 5)

Simplify

- \frac{1}{2} (- 0 + 5 + 0 + 5) : - 5

= - 5

\frac{d}{d x} (ln (a + x 2 a x + x^{2}))

x \to 3 lim (f (x) x)

\frac{d}{d t} (2 t + 4)

\frac{1}{z ^{2}}

x \to - 5 lim (3 x - 1)

What is the limit as x approaches 0 of x/(sqrt(5-x)-\sqrt{5+x)} ?
The limit as x approaches 0 of x/(sqrt(5-x)-\sqrt{5+x)} is -sqrt(5)