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

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

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

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

\frac{1}{n}

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 1

= \frac{1}{n \cdot 1 ^{n - 1}}

Simplify

= \frac{1}{n}

(x + y)^{2} d x + (2 x y + x^{2} - 4) d y = 0

\frac{d}{d x} (5 e^{x} + 3)

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

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

x - y^{2} = 0, x + 2 y^{2} = 3

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