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\(limit( x^3*e^x, x=-inf )\)

also this

\(limit( (x^3+2x)*(cos(3/x^2))), x=0 )\)

Guest Apr 13, 2018

Best Answer 

 #1
avatar+26634 
+2

When x is negative ex goes to zero much faster than x3 goes to -infinity, so:   \(\lim_{x\rightarrow -\infty}(x^3e^x)=0\)

 

The value of cosine is always bounded such that it's magnitude is never greater than 1. 

Hence:   \(\lim_{x\rightarrow 0}((x^3+2x)\cos(3/x^2))=0\) 

 

.

Alan  Apr 13, 2018
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2+0 Answers

 #1
avatar+26634 
+2
Best Answer

When x is negative ex goes to zero much faster than x3 goes to -infinity, so:   \(\lim_{x\rightarrow -\infty}(x^3e^x)=0\)

 

The value of cosine is always bounded such that it's magnitude is never greater than 1. 

Hence:   \(\lim_{x\rightarrow 0}((x^3+2x)\cos(3/x^2))=0\) 

 

.

Alan  Apr 13, 2018
 #2
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I see, thank you very much smiley

Guest Apr 15, 2018

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