What is the limit as x approaches 1 of (x^{11}+2x-3)/(x^7+x^2-x-1) ?

The limit as x approaches 1 of (x^{11}+2x-3)/(x^7+x^2-x-1) is 13/8

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^{11}+2x-3)/(x^7+x^2-x-1)

x \to 1 lim (\frac{x ^{11} + 2 x - 3}{x ^{7} + x ^{2} - x - 1})

\frac{13}{8}

Decimal

1.625

Solution steps

x \to 1 lim (\frac{x ^{11} + 2 x - 3}{x ^{7} + x ^{2} - x - 1})

Simplify

\frac{x ^{11} + 2 x - 3}{x ^{7} + x ^{2} - x - 1} : \frac{x ^{10} + x ^{9} + x ^{8} + x ^{7} + x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 3}{( x + 1 ) ( x ^{5} + x ^{3} + x + 1 )}

= x \to 1 lim (\frac{x ^{10} + x ^{9} + x ^{8} + x ^{7} + x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 3}{( x + 1 ) ( x ^{5} + x ^{3} + x + 1 )})

Plug in the value

x = 1

= \frac{1 ^{10} + 1 ^{9} + 1 ^{8} + 1 ^{7} + 1 ^{6} + 1 ^{5} + 1 ^{4} + 1 ^{3} + 1 ^{2} + 1 + 3}{( 1 + 1 ) ( 1 ^{5} + 1 ^{3} + 1 + 1 )}

Simplify

\frac{1 ^{10} + 1 ^{9} + 1 ^{8} + 1 ^{7} + 1 ^{6} + 1 ^{5} + 1 ^{4} + 1 ^{3} + 1 ^{2} + 1 + 3}{( 1 + 1 ) ( 1 ^{5} + 1 ^{3} + 1 + 1 )} : \frac{13}{8}

= \frac{13}{8}

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{2} - 1})

x \to - 3 lim (\frac{x + 1}{x ^{2} - 9})

x \to 0 lim (cos (x))

x \to \frac{π}{3} lim \frac{( sin ( x ) - \frac{3}{2} )}{x - \frac{π}{3}}

x \to \infty lim (\frac{x ^{3}}{x + 4})

What is the limit as x approaches 1 of (x^{11}+2x-3)/(x^7+x^2-x-1) ?
The limit as x approaches 1 of (x^{11}+2x-3)/(x^7+x^2-x-1) is 13/8