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}

x \to 0 lim (\frac{3 x}{sin ( 10 x )})

\frac{\partial}{\partial x} (3 (y - 1)^{3} (x - 6))

\int \frac{x ^{3}}{x ^{2} + 4 x + 4} d x

\int (x - 1)^{2} - 4 d x

\int (x + 1) (x + 2) d x

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