What is the limit as x approaches (1) of (x^8-1)/(x^5-1) ?

The limit as x approaches (1) of (x^8-1)/(x^5-1) is 8/5

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limit as x approaches (1) of (x^8-1)/(x^5-1)

x \to (1) lim (\frac{x ^{8} - 1}{x ^{5} - 1})

\frac{8}{5}

Decimal

1.6

Solution steps

x \to 1 lim (\frac{x ^{8} - 1}{x ^{5} - 1})

Simplify

\frac{x ^{8} - 1}{x ^{5} - 1} : \frac{( x ^{2} + 2 x + 1 ) ( x ^{2} - 2 x + 1 ) ( x ^{2} + 1 ) ( x + 1 )}{x ^{4} + x ^{3} + x ^{2} + x + 1}

= x \to 1 lim (\frac{( x ^{2} + 2 x + 1 ) ( x ^{2} - 2 x + 1 ) ( x ^{2} + 1 ) ( x + 1 )}{x ^{4} + x ^{3} + x ^{2} + x + 1})

Plug in the value

x = 1

= \frac{( 1 ^{2} + 2 \cdot 1 + 1 ) ( 1 ^{2} - 2 \cdot 1 + 1 ) ( 1 ^{2} + 1 ) ( 1 + 1 )}{1 ^{4} + 1 ^{3} + 1 ^{2} + 1 + 1}

Simplify

\frac{( 1 ^{2} + 2 \cdot 1 + 1 ) ( 1 ^{2} - 2 \cdot 1 + 1 ) ( 1 ^{2} + 1 ) ( 1 + 1 )}{1 ^{4} + 1 ^{3} + 1 ^{2} + 1 + 1} : \frac{8}{5}

= \frac{8}{5}

What is the limit as x approaches (1) of (x^8-1)/(x^5-1) ?
The limit as x approaches (1) of (x^8-1)/(x^5-1) is 8/5