What is the limit as x approaches 1 of (x^7-x)/(x-1) ?

The limit as x approaches 1 of (x^7-x)/(x-1) is 6

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limit as x approaches 1 of (x^7-x)/(x-1)

x \to 1 lim (\frac{x ^{7} - x}{x - 1})

6

Solution steps

x \to 1 lim (\frac{x ^{7} - x}{x - 1})

Simplify

\frac{x ^{7} - x}{x - 1} : x (x + 1) (x^{4} + x^{2} + 1)

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

Plug in the value

x = 1

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

Simplify

= 6

What is the limit as x approaches 1 of (x^7-x)/(x-1) ?
The limit as x approaches 1 of (x^7-x)/(x-1) is 6