What is the limit as x approaches 1+of (2+x)/(1-x) ?

The limit as x approaches 1+of (2+x)/(1-x) is -infinity

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limit as x approaches 1+of (2+x)/(1-x)

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

- \infty

Solution steps

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

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

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

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

x \to 1 + lim (2 + x) = 3

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

= 3 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to 3 lim (2 - \frac{1}{x})

\frac{d}{d x} (sin (\frac{1}{5} x))

x \to 2 lim (2 x + 3)

tan (2 (x + 1))

\frac{d}{d t} (\frac{1 - e ^{- 2 t}}{t})

What is the limit as x approaches 1+of (2+x)/(1-x) ?
The limit as x approaches 1+of (2+x)/(1-x) is -infinity