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

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

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

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

\frac{2}{h ( 0 )}

Solution steps

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

Plug in the value

x = 0

, assuming the function is continuous at this point

= \frac{2 ( 0 + h ( 0 ) ) - 2 \cdot 0}{h ( 0 )}

Simplify

\frac{2 ( 0 + h ( 0 ) ) - 2 \cdot 0}{h ( 0 )} : \frac{2}{h ( 0 )}

= \frac{2}{h ( 0 )}

y^{^{''}} + y = 0, y (0) = 1, y^{^{'}} (0) = 1

5 t^{3}

f (t) = 6 cos (2 t)

\frac{d}{d x} (256 cos (2 x))

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