What is the limit as x approaches 63 of (sqrt(x+1)-8)/(x-63) ?

The limit as x approaches 63 of (sqrt(x+1)-8)/(x-63) is 1/16

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limit as x approaches 63 of (sqrt(x+1)-8)/(x-63)

x \to 63 lim (\frac{x + 1 - 8}{x - 63})

\frac{1}{16}

Decimal Notation

0.0625

Solution steps

x \to 63 lim (\frac{x + 1 - 8}{x - 63})

Rationalize numerator

\frac{x + 1 - 8}{x - 63} : \frac{1}{x + 1 + 8}

= x \to 63 lim (\frac{1}{x + 1 + 8})

Plug in the value

x = 63

= \frac{1}{63 + 1 + 8}

Simplify

\frac{1}{63 + 1 + 8} : \frac{1}{16}

= \frac{1}{16}

x \to 1 + lim (\frac{1}{tan ( x - 1 )})

x \to 0 lim (e^{x} + x)

x \to 0 lim (sin (\frac{3 x}{x}))

What is the limit as x approaches 63 of (sqrt(x+1)-8)/(x-63) ?
The limit as x approaches 63 of (sqrt(x+1)-8)/(x-63) is 1/16