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

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

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

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

\infty

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

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

x \to - 1 + lim (1) = 1

= \infty - 1

Apply Infinity Property:

\infty - c = \infty

= \infty

x \to \frac{π}{2} lim (sin (\frac{π}{2}))

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

x \to 0 lim (\frac{x - 2}{\frac{1}{x}})

t \to 1 lim (\frac{t - 1}{t})

n \to \infty lim (e^{0})

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