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Numerade Educator

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Problem 4 Medium Difficulty

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).

$ \displaystyle \lim_{x \to -1}(x^4 - 3x)(x^2 + 5x + 3) $

Answer

$-4$

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Video Transcript

we have a question in which we have people with the limit Limit acceptances to -1. Excellent. Really powerful minus three X and two X square plus five X. Let's see um By indicating proper limit laws and it is so let us pay attention on the law that if limit access approaching to a if we have fx and gx static product. So this can be written as limit X approaches to a fx into limit X approaches to a gxe. So let us use this. It will become Limit x approaches to -1 Exodus depart for -3 x. into limit Except for just 2 -1 at the square Plus five x plus three. No, if they use that limit X approaches to this is law will be we will use affects place G X. So this could building has a limit X approaches to a fx bless limit X approaches to a dx. So here we will be applying in both the cases this law limit X approaches to -1 x rays to depart for place Limit x approaches to -1 minus three X. Yeah limit X approaches to minus one X squared Plus limit x approaches to -15 x Plus limit x approaches to -1. Okay, okay so there is another law that if lim X approaches to a and if any function affects is multiplied with any constant term lambda. So the school Britain has limits, linda, lim X approaches to fx. It will be utilized this here. This will become limit X approaches to minus one. Access to the part four plus minus three is a constant 2 -3 limit x approaches to -1 X Limit x approaches to -1 x esquire Yes five limit X approaches to -1 x. Less limit X approaches to -1 to think it's not plugging in minus one in place of acts everywhere minus one, there's depart for plus minus three to minus one Into -1 whole square Plus five and 2 -1 Plus three because this is constant and limited constant. Is that constant? Only this is the law limit X approaches to a linda will be simply linda. Okay so this is one last three, 10 to one minus five plus three, so for into minus one That is -4 -4 should be uh answer thank you. Okay.