What is the limit as x approaches 1 of [(x^3-1)/(x^2-1)] ?

The limit as x approaches 1 of [(x^3-1)/(x^2-1)] is 3/2

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limit as x approaches 1 of [(x^3-1)/(x^2-1)]

x \to 1 lim ([\frac{x ^{3} - 1}{x ^{2} - 1}])

\frac{3}{2}

Decimal

1.5

Solution steps

x \to 1 lim (\frac{x ^{3} - 1}{x ^{2} - 1})

Simplify

\frac{x ^{3} - 1}{x ^{2} - 1} : \frac{x ^{2} + x + 1}{x + 1}

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

Plug in the value

x = 1

= \frac{1 ^{2} + 1 + 1}{1 + 1}

Simplify

= \frac{3}{2}

x \to 1 lim (\frac{5 x + 3 x - 2}{x ^{2} - 1})

x \to 0 lim (\frac{( 1 - cos ^{2} ( x ) )}{ln ( 1 + x ^{2} )})

x \to 0 lim (x^{9} e^{- x^{8}})

x \to 1 lim (2 x + 2)

x \to - 3 - lim (\frac{2 x}{x - 3})

What is the limit as x approaches 1 of [(x^3-1)/(x^2-1)] ?
The limit as x approaches 1 of [(x^3-1)/(x^2-1)] is 3/2