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

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

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

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

m

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 1

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

Simplify

= m

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