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

x \to 8 - lim (\frac{- 7}{x ^{2} - 8 x})

x \to 0 lim (1 + 2 x)

x \to 0 lim (3 x csc (x))

x \to 0 + lim (x^{3} sin (\frac{1}{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