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

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

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

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

- \infty

Solution steps

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

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

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

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

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

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

= 3 (- \infty)

Apply Infinity Property:

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

= - \infty

6 cos (θ) + 3 sin^{2} (θ)

- 2 x (x^{2} + 1)^{- 2}

x - 2^{- x}

\frac{u}{u + \frac{c}{u}}

\int (sin (x + y)) d x

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