What is the limit as x approaches 1+of (x^2-4)/(x-1) ?

The limit as x approaches 1+of (x^2-4)/(x-1) is -infinity

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limit as x approaches 1+of (x^2-4)/(x-1)

x \to 1 + lim (\frac{x ^{2} - 4}{x - 1})

- \infty

Solution steps

x \to 1 + lim (\frac{x ^{2} - 4}{x - 1})

\frac{x ^{2} - 4}{x - 1} = (x^{2} - 4) \frac{1}{x - 1}

= x \to 1 + lim ((x^{2} - 4) \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} - 4) \cdot x \to 1 + lim (\frac{1}{x - 1})

x \to 1 + lim (x^{2} - 4) = - 3

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

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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What is the limit as x approaches 1+of (x^2-4)/(x-1) ?
The limit as x approaches 1+of (x^2-4)/(x-1) is -infinity