What is the limit as x approaches 6 of (2-sqrt(x-2))/(36-x^2) ?

The limit as x approaches 6 of (2-sqrt(x-2))/(36-x^2) is 1/48

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limit as x approaches 6 of (2-sqrt(x-2))/(36-x^2)

x \to 6 lim (\frac{2 - x - 2}{36 - x ^{2}})

\frac{1}{48}

Decimal

0.02083 \dots

Solution steps

x \to 6 lim (\frac{2 - x - 2}{36 - x ^{2}})

Multiply by the conjugate of

2 - x - 2 : \frac{- x + 6}{2 + x - 2}

= x \to 6 lim (\frac{\frac{- x + 6}{2 + x - 2}}{36 - x ^{2}})

Simplify

\frac{\frac{- x + 6}{2 + x - 2}}{36 - x ^{2}} : \frac{1}{( x - 2 + 2 ) ( x + 6 )}

= x \to 6 lim (\frac{1}{( x - 2 + 2 ) ( x + 6 )})

Plug in the value

x = 6

= \frac{1}{( 6 - 2 + 2 ) ( 6 + 6 )}

Simplify

\frac{1}{( 6 - 2 + 2 ) ( 6 + 6 )} : \frac{1}{48}

= \frac{1}{48}

x \to - 2 lim (2 x - 4)

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

x \to 0 + lim (\frac{x ^{2} + 3 x + 4}{x})

x \to - 3 lim (x^{3} - 3 x - 7)

x \to 0 lim (\frac{e ^{x^{2}} - cos ( x )}{sin ^{2} ( x ) + 3 sin ^{5} ( x )})

What is the limit as x approaches 6 of (2-sqrt(x-2))/(36-x^2) ?
The limit as x approaches 6 of (2-sqrt(x-2))/(36-x^2) is 1/48