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}) = 1

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

= 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 0 + lim (x^{2} ln (x^{3}))

x \to \infty lim (\frac{x ^{2} - 5 x + 4}{4 x ^{2} + 2 x})

x \to \infty lim (- \frac{x}{0})

n \to \infty lim (e^{- n + 2})

h \to 0 lim (csc (h) - cot (h))

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