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

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

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

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

7

Solution steps

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

Simplify

\frac{x ^{7} - 1}{x - 1} : x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1

= x \to 1 lim (x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1)

Plug in the value

x = 1

= 1^{6} + 1^{5} + 1^{4} + 1^{3} + 1^{2} + 1 + 1

Simplify

= 7

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