What is the limit as x approaches (1) of (x^8-1)/(x^5-1) ?

The limit as x approaches (1) of (x^8-1)/(x^5-1) is 8/5

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 (x^8-1)/(x^5-1)

x \to (1) lim (\frac{x ^{8} - 1}{x ^{5} - 1})

\frac{8}{5}

Decimal Notation

1.6

Solution steps

x \to 1 lim (\frac{x ^{8} - 1}{x ^{5} - 1})

Simplify

\frac{x ^{8} - 1}{x ^{5} - 1} : \frac{( x ^{2} + 2 x + 1 ) ( x ^{2} - 2 x + 1 ) ( x ^{2} + 1 ) ( x + 1 )}{x ^{4} + x ^{3} + x ^{2} + x + 1}

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

Plug in the value

x = 1

= \frac{( 1 ^{2} + 2 \cdot 1 + 1 ) ( 1 ^{2} - 2 \cdot 1 + 1 ) ( 1 ^{2} + 1 ) ( 1 + 1 )}{1 ^{4} + 1 ^{3} + 1 ^{2} + 1 + 1}

Simplify

\frac{( 1 ^{2} + 2 \cdot 1 + 1 ) ( 1 ^{2} - 2 \cdot 1 + 1 ) ( 1 ^{2} + 1 ) ( 1 + 1 )}{1 ^{4} + 1 ^{3} + 1 ^{2} + 1 + 1} : \frac{8}{5}

= \frac{8}{5}

\int \frac{6 ( 1 + s )}{s ( s ^{2} + 7 s + 6 )} d s

\int 1 - z^{2}

\int \frac{x ^{3} + x}{x - 1} d x

h \to 0 lim (\frac{1}{h})

y = (3 - x^{2}) (x^{3} - 3 x + 2)

What is the limit as x approaches (1) of (x^8-1)/(x^5-1) ?
The limit as x approaches (1) of (x^8-1)/(x^5-1) is 8/5