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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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})

= 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

f (x) = \frac{x ^{2}}{x - 3}, at x = 0

\frac{\partial}{\partial x} (cos (x + 9 y))

y d y = x d x

\frac{d}{d y} (9 - y^{2})

\frac{d}{d x} (2^{x} + 2 cos (\frac{2 x}{2}))

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