Question #0404c

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Answer 1 · 2017-11-07T14:38:14

$lim_(x to oo)(1-x^3)/(2x+2)=-oo$

The limit is $lim_(x to oo)(1-x^3)/(2x+2)$

Here we let $x=oo$ then $(1-x^3)/(2x+2)=(-oo)/(oo)=$ Undefined

So therefore we can apply the L'Hospital's rule in which we differentiate the numerator and denominator individually with respect to $x$

$lim_(x to oo)(d/dx(1-x^3))/(d/dx(2x+2))$

$lim_(x to oo)(-3x^2)/2$

Now when we let $x=oo$ , we get

$lim_(x to oo)(-3x^2)/2=(-3oo^2)/2$

$(-3oo^2)/2$ will always equal $-oo$ as $oo$ is not an actual number, just a concept.

So finally, $lim_(x to oo)(1-x^3)/(2x+2)=-oo$

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