What is the limit as x approaches 11 of (3x-33)/(sqrt(11x)-11) ?

The limit as x approaches 11 of (3x-33)/(sqrt(11x)-11) is 6

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limit as x approaches 11 of (3x-33)/(sqrt(11x)-11)

x \to 11 lim (\frac{3 x - 33}{11 x - 11})

6

Solution steps

x \to 11 lim (\frac{3 x - 33}{11 x - 11})

Rationalize denominator

\frac{3 x - 33}{11 x - 11} : \frac{3 ( 11 x + 11 )}{11}

= x \to 11 lim (\frac{3 ( 11 x + 11 )}{11})

Plug in the value

x = 11

= \frac{3 ( 11 11 + 11 )}{11}

Simplify

\frac{3 ( 11 11 + 11 )}{11} : 6

= 6

e^{- s} (\frac{1}{s ^{2}} - \frac{1}{s})

\frac{d y}{d x}, 5 e^{x y} - 4 x = y + 30.9

\frac{d}{d x} ((8 x)^{\frac{1}{2}})

\frac{\partial}{\partial x} (3 \cdot (y + 1) \cdot (x - 3)^{3})

\int (x^{2} - 4)^{3} x d x

What is the limit as x approaches 11 of (3x-33)/(sqrt(11x)-11) ?
The limit as x approaches 11 of (3x-33)/(sqrt(11x)-11) is 6