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

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

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

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

n

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 1

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

Simplify

= n

x \to 5 + lim (\frac{- 2}{x ^{2} - 25})

\int x^{2} (x + 3) d x

x^{2} + y^{2} = 25, (4, 3)

\frac{\partial}{\partial x} (4 z^{5} + x^{4} y - y^{5} x)

\int (sin (t) cos (t)) d t

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