What is the limit as y approaches 1 of (y-1)/(y^6-1) ?

The limit as y approaches 1 of (y-1)/(y^6-1) is 1/6

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limit as y approaches 1 of (y-1)/(y^6-1)

y \to 1 lim (\frac{y - 1}{y ^{6} - 1})

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

y \to 1 lim (\frac{y - 1}{y ^{6} - 1})

Simplify

\frac{y - 1}{y ^{6} - 1} : \frac{1}{( y + 1 ) ( y ^{4} + y ^{2} + 1 )}

= y \to 1 lim (\frac{1}{( y + 1 ) ( y ^{4} + y ^{2} + 1 )})

Plug in the value

y = 1

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

Simplify

= \frac{1}{6}

ln (2 x + 3)

\frac{d}{d x} (\frac{8}{sin ( x )} + \frac{1}{cot ( x )})

\int_{0}^{\frac{π}{2}} cos^{2} (2 x) d x

sin^{4} (\frac{x}{4}) + cos^{4} (\frac{x}{4})

\frac{\partial}{\partial x} (x y + y + 2 x + 2)

What is the limit as y approaches 1 of (y-1)/(y^6-1) ?
The limit as y approaches 1 of (y-1)/(y^6-1) is 1/6