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 Calculus help

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I do not know how to type the correct format for this problem so I will put into words and you can write it in symbols.

 

The limit of (x^3+5x)/(2x^3-x^2+4) as x approaches infinity is what?  If anyone knows how to solve this problem and can give me step-by-step instructions, I would really appreciate it.  Thanks.

 Apr 13, 2018

2+0 Answers

 #1
avatar+37155 
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https://www.symbolab.com/solver/limit-calculator/%5Clim_%7Bx%5Cto%5Cinfty%7D%20%5Cfrac%7B%5Cleft(x%5E%7B3%7D%2B5x%5Cright)%7D%7B%5Cleft(2x%5E%7B3%7D-x%5E%7B2%7D%2B4%5Cright)%7D

 Apr 14, 2018
edited by ElectricPavlov  Apr 14, 2018
 #2
avatar+33661 
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As x tends to infinity, in the numerator 5x becomes negligible compared to x^3.  In the denominator x^2 and 4 become negligible compared to x^3 Hence the expression tends to x^3/(2x^3).  The x^3 terms cancel leaving 1/2 as the limiting value.

 

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 Apr 14, 2018
edited by Alan  Apr 14, 2018

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