What is the limit as x approaches 1 of sqrt((x^5-1)/(x-1)) ?

The limit as x approaches 1 of sqrt((x^5-1)/(x-1)) is square root of 5

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 sqrt((x^5-1)/(x-1))

x \to 1 lim (\frac{x ^{5} - 1}{x - 1})

5

Solution steps

x \to 1 lim (\frac{x ^{5} - 1}{x - 1})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= x \to 1 lim (\frac{x ^{5} - 1}{x - 1})

Simplify

\frac{x ^{5} - 1}{x - 1} : x^{4} + x^{3} + x^{2} + x + 1

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

Plug in the value

x = 1

= 1^{4} + 1^{3} + 1^{2} + 1 + 1

Simplify

= 5

\frac{d}{d x} (sin (\frac{π x}{4}))

\frac{1}{x}, 1

6 sin (4 x)

\int_{1}^{2} 6 x^{2} d x

\int 3 e^{- 0.5 x} d x

What is the limit as x approaches 1 of sqrt((x^5-1)/(x-1)) ?
The limit as x approaches 1 of sqrt((x^5-1)/(x-1)) is square root of 5