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

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

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

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

- \infty

Solution steps

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

\frac{x ^{2}}{1 - x} = x^{2} \frac{1}{1 - x}

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

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

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

= 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

\int x e^{- x} d x

\int cos (x) e^{- x} d x

y = 3 x, y = 5 x^{2}

\frac{d ^{2}}{d x ^{2}} (x e^{7 x})

\int \frac{5 x ^{2}}{x ^{2} - 4} d x

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