To determine

To evaluate: limx→∞x3e−x2

Answer

limx→∞x3e−x2=0

Explanation

The following limit is in indeterminate form, Applying l’Hospital’s Rule, we get

limx→∞x3e−x2=limx→∞x3ex2=limx→∞3x2ex2×2x=32limx→∞xex2=32limx→∞1ex2×2x=34limx→∞1ex2x=34(0)=0

Conclusion: The value of the limit is limx→∞x3e−x2=0