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

also this

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

Guest Apr 13, 2018

#1**+2 **

Best Answer

When x is negative e^{x} goes to zero much faster than x^{3} 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