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

The limit as x approaches 2-of-2/(sqrt(2-x)) is -infinity

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limit as x approaches 2-of-2/(sqrt(2-x))

x \to 2 - lim (- \frac{2}{2 - x})

- \infty

Solution steps

x \to 2 - lim (- \frac{2}{2 - x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

For

x

approaching

2

from the left

, x < 2 \Rightarrow 2 - x > 0

The denominator is a positive quantity approaching 0 from the right

= - 2 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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

\frac{\partial}{\partial x} (x^{3} - 3 x y^{2})

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

\int \frac{1}{2 x - 1} d x

\frac{d}{d x} (\frac{5 1 - x ^{3}}{6})

What is the limit as x approaches 2-of-2/(sqrt(2-x)) ?
The limit as x approaches 2-of-2/(sqrt(2-x)) is -infinity