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