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

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

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

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

- \infty

Solution steps

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

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

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

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

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

= (e + 1) (- \infty)

Apply Infinity Property:

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

= - \infty

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