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

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

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

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

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

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

Simplify

= \frac{1}{6}

y^{^{''}} + 4 y = t^{2}

f (x) = e^{\infty}

(5 x^{2} - 2 x + 4) (4 x^{2} + 3 x - 6)

\int - x^{2} + 6 d x

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

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