What is the limit as x approaches 1 of (x^{10}-1)/(x-1) ?

The limit as x approaches 1 of (x^{10}-1)/(x-1) is 10

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limit as x approaches 1 of (x^{10}-1)/(x-1)

x \to 1 lim (\frac{x ^{10} - 1}{x - 1})

10

Solution steps

x \to 1 lim (\frac{x ^{10} - 1}{x - 1})

Simplify

\frac{x ^{10} - 1}{x - 1} : (x + 1) (x^{4} - x^{3} + x^{2} - x + 1) (x^{4} + x^{3} + x^{2} + x + 1)

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

Plug in the value

x = 1

= (1 + 1) (1^{4} - 1^{3} + 1^{2} - 1 + 1) (1^{4} + 1^{3} + 1^{2} + 1 + 1)

Simplify

(1 + 1) (1^{4} - 1^{3} + 1^{2} - 1 + 1) (1^{4} + 1^{3} + 1^{2} + 1 + 1) : 10

= 10

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

\frac{d}{d x} (x e^{2 x})

x \to \infty lim (a^{- x})

\frac{\partial}{\partial x} (\frac{3 x + y}{z})

\frac{d}{d x} (11 x arcsin (x))

What is the limit as x approaches 1 of (x^{10}-1)/(x-1) ?
The limit as x approaches 1 of (x^{10}-1)/(x-1) is 10