What is the limit as h approaches 0 of (sqrt(13x-h)-sqrt(13x))/h ?

The limit as h approaches 0 of (sqrt(13x-h)-sqrt(13x))/h is -1/(2sqrt(13)\sqrt{x)}

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limit as h approaches 0 of (sqrt(13x-h)-sqrt(13x))/h

h \to 0 lim (\frac{13 x - h - 13 x}{h})

- \frac{1}{2 13 x}

Solution steps

h \to 0 lim (\frac{13 x - h - 13 x}{h})

Multiply by the conjugate of

13 x - h - 13 x : \frac{- h}{13 x - h + 13 x}

= h \to 0 lim (\frac{\frac{- h}{13 x - h + 13 x}}{h})

Simplify

\frac{\frac{- h}{13 x - h + 13 x}}{h} : - \frac{1}{- h + 13 x + 13 x}

= h \to 0 lim (- \frac{1}{- h + 13 x + 13 x})

Plug in the value

h = 0

= - \frac{1}{- 0 + 13 x + 13 x}

Simplify

- \frac{1}{- 0 + 13 x + 13 x} : - \frac{1}{2 13 x}

= - \frac{1}{2 13 x}

\int \frac{x ^{3}}{( 1 - 16 x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim (10 x)

\frac{d}{d x} (sec (2 x))

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

\frac{d}{d x} (\frac{x x ^{2} + 1}{( 2 x + 1 ) ^{2}})

What is the limit as h approaches 0 of (sqrt(13x-h)-sqrt(13x))/h ?
The limit as h approaches 0 of (sqrt(13x-h)-sqrt(13x))/h is -1/(2sqrt(13)\sqrt{x)}