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

= 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