What is the limit as x approaches 1+of (x+5)/(1-x^2) ?

The limit as x approaches 1+of (x+5)/(1-x^2) is -infinity

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limit as x approaches 1+of (x+5)/(1-x^2)

x \to 1 + lim (\frac{x + 5}{1 - x ^{2}})

- \infty

Solution steps

x \to 1 + lim (\frac{x + 5}{1 - x ^{2}})

\frac{x + 5}{1 - x ^{2}} = (x + 5) \frac{1}{1 - x ^{2}}

= x \to 1 + lim ((x + 5) \frac{1}{1 - x ^{2}})

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 + 5) \cdot x \to 1 + lim (\frac{1}{1 - x ^{2}})

x \to 1 + lim (x + 5) = 6

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

= 6 (- \infty)

Apply Infinity Property:

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

= - \infty

What is the limit as x approaches 1+of (x+5)/(1-x^2) ?
The limit as x approaches 1+of (x+5)/(1-x^2) is -infinity