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

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

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

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

8

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

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

Simplify

(1^{2} + 2 \cdot 1 + 1) (1^{2} - 2 \cdot 1 + 1) (1^{2} + 1) (1 + 1) : 8

= 8

n = 1 \sum \infty \frac{( 3 ^{n - 1} )}{9 ^{n}}

\frac{d}{d x} (4 x 16 - x^{2})

\int_{1}^{2} 2 x x^{2} + 1 d x

n = 3 \sum \infty \frac{1}{3 ^{n}}

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 3 y^{3})

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