What is the limit as x approaches 0 of (sqrt(x+36)-6)/x ?

The limit as x approaches 0 of (sqrt(x+36)-6)/x is 1/12

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limit as x approaches 0 of (sqrt(x+36)-6)/x

x \to 0 lim (\frac{x + 36 - 6}{x})

\frac{1}{12}

Decimal Notation

0.08333 \dots

Solution steps

x \to 0 lim (\frac{x + 36 - 6}{x})

Rationalize numerator

\frac{x + 36 - 6}{x} : \frac{1}{x + 36 + 6}

= x \to 0 lim (\frac{1}{x + 36 + 6})

Plug in the value

x = 0

= \frac{1}{0 + 36 + 6}

Simplify

\frac{1}{0 + 36 + 6} : \frac{1}{12}

= \frac{1}{12}

\frac{- x ^{2}}{y ^{2}}

- 4 x^{2}

y^{^{'}} = \frac{3 y - 4 x}{2 y - 3 x}

\int x y d y

y = 3 x, x + y = 4, y = 1, y = 0

What is the limit as x approaches 0 of (sqrt(x+36)-6)/x ?
The limit as x approaches 0 of (sqrt(x+36)-6)/x is 1/12