What is the limit as x approaches-1 of (x^6-1)/(x+1) ?

The limit as x approaches-1 of (x^6-1)/(x+1) is -6

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limit as x approaches-1 of (x^6-1)/(x+1)

x \to - 1 lim (\frac{x ^{6} - 1}{x + 1})

- 6

Solution steps

x \to - 1 lim (\frac{x ^{6} - 1}{x + 1})

Simplify

\frac{x ^{6} - 1}{x + 1} : (x - 1) (x^{4} + x^{2} + 1)

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

Plug in the value

x = - 1

= (- 1 - 1) ((- 1)^{4} + (- 1)^{2} + 1)

Simplify

(- 1 - 1) ((- 1)^{4} + (- 1)^{2} + 1) : - 6

= - 6

What is the limit as x approaches-1 of (x^6-1)/(x+1) ?
The limit as x approaches-1 of (x^6-1)/(x+1) is -6