What is the limit as x approaches 58 of (sqrt(x+6)-8)/(x-58) ?

The limit as x approaches 58 of (sqrt(x+6)-8)/(x-58) is 1/16

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limit as x approaches 58 of (sqrt(x+6)-8)/(x-58)

x \to 58 lim (\frac{x + 6 - 8}{x - 58})

\frac{1}{16}

Decimal

0.0625

Solution steps

x \to 58 lim (\frac{x + 6 - 8}{x - 58})

Rationalize numerator

\frac{x + 6 - 8}{x - 58} : \frac{1}{x + 6 + 8}

= x \to 58 lim (\frac{1}{x + 6 + 8})

Plug in the value

x = 58

= \frac{1}{58 + 6 + 8}

Simplify

\frac{1}{58 + 6 + 8} : \frac{1}{16}

= \frac{1}{16}

What is the limit as x approaches 58 of (sqrt(x+6)-8)/(x-58) ?
The limit as x approaches 58 of (sqrt(x+6)-8)/(x-58) is 1/16