What is the limit as x approaches 1 of (x^{1/4}-1)/(x^{1/3)-1} ?

The limit as x approaches 1 of (x^{1/4}-1)/(x^{1/3)-1} is 3/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 1 of (x^{1/4}-1)/(x^{1/3)-1}

x \to 1 lim (\frac{x ^{\frac{1}{4}} - 1}{x ^{\frac{1}{3}} - 1})

\frac{3}{4}

Decimal

0.75

Solution steps

x \to 1 lim (\frac{x ^{\frac{1}{4}} - 1}{x ^{\frac{1}{3}} - 1})

Apply L'Hopital's Rule

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

Plug in the value

x = 1

= \frac{\frac{1}{4 \cdot 1 ^{\frac{3}{4}}}}{\frac{1}{3 \cdot 1 ^{\frac{2}{3}}}}

Simplify

\frac{\frac{1}{4 \cdot 1 ^{\frac{3}{4}}}}{\frac{1}{3 \cdot 1 ^{\frac{2}{3}}}} : \frac{3}{4}

= \frac{3}{4}

What is the limit as x approaches 1 of (x^{1/4}-1)/(x^{1/3)-1} ?
The limit as x approaches 1 of (x^{1/4}-1)/(x^{1/3)-1} is 3/4