What is the limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x) ?

The limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x) is 1/(4sqrt(5))

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limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x)

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

\frac{1}{4 5}

Solution steps

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

Rationalize numerator

\frac{5 + x - 5}{x} : \frac{1}{x + 5 + 5}

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

Plug in the value

x = 0

= \frac{1}{2} \cdot \frac{1}{0 + 5 + 5}

Simplify

\frac{1}{2} \cdot \frac{1}{0 + 5 + 5} : \frac{1}{4 5}

= \frac{1}{4 5}

f (t) = e^{7 t s i n (2 t)}

f (x) = x (27 x^{- 2} + 2), at x = - 3

\frac{\partial}{\partial x} (\frac{x - 1}{x + 1})

\int_{0}^{\infty} \frac{1}{e ^{x} - 1} d x

\frac{d}{d t} (\frac{1}{6} t^{3})

What is the limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x) ?
The limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x) is 1/(4sqrt(5))