What is the limit as x approaches 1 of (x^4-1)/(x^3-1) ?

The limit as x approaches 1 of (x^4-1)/(x^3-1) is 4/3

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limit as x approaches 1 of (x^4-1)/(x^3-1)

x \to 1 lim (\frac{x ^{4} - 1}{x ^{3} - 1})

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

x \to 1 lim (\frac{x ^{4} - 1}{x ^{3} - 1})

Simplify

\frac{x ^{4} - 1}{x ^{3} - 1} : \frac{( x ^{2} + 1 ) ( x + 1 )}{x ^{2} + x + 1}

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

Plug in the value

x = 1

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

Simplify

\frac{( 1 ^{2} + 1 ) ( 1 + 1 )}{1 ^{2} + 1 + 1} : \frac{4}{3}

= \frac{4}{3}

What is the limit as x approaches 1 of (x^4-1)/(x^3-1) ?
The limit as x approaches 1 of (x^4-1)/(x^3-1) is 4/3