What is the limit as x approaches 1 of (x-1)/(x^4-1) ?

The limit as x approaches 1 of (x-1)/(x^4-1) is 1/4

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limit as x approaches 1 of (x-1)/(x^4-1)

x \to 1 lim (\frac{x - 1}{x ^{4} - 1})

\frac{1}{4}

Decimal Notation

0.25

Solution steps

x \to 1 lim (\frac{x - 1}{x ^{4} - 1})

Simplify

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

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

Plug in the value

x = 1

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

Simplify

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

= \frac{1}{4}

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

x \to 3 lim (\frac{x}{x ^{2} - 4 x + 3})

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

x \to 0 lim (\frac{3 x - 1}{x})

x \to 0 lim (400 x + 104000)

What is the limit as x approaches 1 of (x-1)/(x^4-1) ?
The limit as x approaches 1 of (x-1)/(x^4-1) is 1/4