What is the limit as x approaches 5+of (2-x)/(x-5) ?

The limit as x approaches 5+of (2-x)/(x-5) is -infinity

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limit as x approaches 5+of (2-x)/(x-5)

x \to 5 + lim (\frac{2 - x}{x - 5})

- \infty

Solution steps

x \to 5 + lim (\frac{2 - x}{x - 5})

\frac{2 - x}{x - 5} = (2 - x) \frac{1}{x - 5}

= x \to 5 + lim ((2 - x) \frac{1}{x - 5})

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

With the exception of indeterminate form

= x \to 5 + lim (2 - x) \cdot x \to 5 + lim (\frac{1}{x - 5})

x \to 5 + lim (2 - x) = - 3

x \to 5 + lim (\frac{1}{x - 5}) = \infty

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int - 4 x (- 6 x^{2} - 1)^{6} d x

\frac{d}{d x} (x^{2} - \frac{2}{3} x^{3})

\frac{\partial}{\partial x} (x e^{x})

\frac{d}{d x} (2 x^{2} e^{\frac{x}{2}})

\frac{( s - 2 )}{s ^{2} - 2 s + 10}

What is the limit as x approaches 5+of (2-x)/(x-5) ?
The limit as x approaches 5+of (2-x)/(x-5) is -infinity