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

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

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limit as y approaches 1 of (y^{11}+2y-3)/(y^7+y^2-y-1)

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

\frac{13}{8}

Decimal Notation

1.625

Solution steps

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

Simplify

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

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

Plug in the value

y = 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 1 lim (3 x + 2)

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

x \to 0 lim (\frac{1 - sin ( x )}{x})

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

x \to \infty lim (ln (x^{\frac{2}{x}}))

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