What is the limit as z approaches 1 of (z-1)/(z^2-1) ?

The limit as z approaches 1 of (z-1)/(z^2-1) is 1/2

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limit as z approaches 1 of (z-1)/(z^2-1)

z \to 1 lim (\frac{z - 1}{z ^{2} - 1})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

z \to 1 lim (\frac{z - 1}{z ^{2} - 1})

Simplify

\frac{z - 1}{z ^{2} - 1} : \frac{1}{z + 1}

= z \to 1 lim (\frac{1}{z + 1})

Plug in the value

z = 1

= \frac{1}{1 + 1}

Simplify

= \frac{1}{2}

\int_{0}^{\frac{π}{6}} x tan^{2} (2 x) d x

x \to 0 lim (e^{3 x} - 1 - 3 x)

\frac{1}{4 x ^{4}}

\frac{d y}{d x} = 4 (x^{2} + 1), x (\frac{π}{4}) = 1

\int (8 x^{3} + \frac{1}{x ^{2}}) d x

What is the limit as z approaches 1 of (z-1)/(z^2-1) ?
The limit as z approaches 1 of (z-1)/(z^2-1) is 1/2