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

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

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

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

- \infty

Solution steps

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

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

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

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

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

= 2 (- \infty)

Apply Infinity Property:

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

= - \infty

y = \frac{- 8 x}{x ^{2} + 1}, (0, 0)

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\frac{\partial}{\partial x} (x^{4} y^{3} - y^{4})

\frac{d}{d y} (ln (x + 2 y + 3 z))

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