Evaluate $lim _(x ->1) (x^4-1)/(x-1)$ ?

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Answer 1 · 2018-03-08T08:26:22

$+-oo$

If you mean it that way...
$lim_(x->1)(x^4-1/(x-1))=+-oo$

It is $+oo$ if you start with $x>1$ and $-oo$ if you start with $x<1$

Answer 2 · 2018-03-08T08:31:47

4

$lim_(x->1) (x^4-1)/(x-1)$

$=>lim_(x->1) [(x^2)^2-(1^2)^2]/(x-1)$

$=>lim_(x->1) [(x^2-1)(x^2+1)]/(x-1)$

$=>lim_(x->1) [(x^2-1^2)(x^2+1)]/(x-1)$

$=>lim_(x->1) [cancel((x-1))(x+1)(x^2+1)]/cancel(x-1)$

$=>lim_(x->1) (x+1)(x^2+1)$

$=> (1+1)(1^1+1)$

$=> 2(1+1)$

$=> 2(2)$

$=> 4$

Evaluate lim _(x ->1) (x^4-1)/(x-1)lim _(x ->1) (x^4-1)/(x-1) ?