How to Solve the Limit lim x→-∞: x²e^x?

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SUMMARY

The limit lim x→-∞: x²e^x can be effectively solved using L'Hôpital's Rule. The original expression can be rewritten as lim x→-∞: x²/e^(-x), which is an indeterminate form of type ∞/∞. By applying L'Hôpital's Rule, the limit converges to 0, confirming that the limit evaluates to 0 as x approaches negative infinity.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with L'Hôpital's Rule
  • Knowledge of exponential functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the application of L'Hôpital's Rule in various limit problems
  • Explore the behavior of exponential functions as x approaches negative infinity
  • Learn about indeterminate forms in calculus
  • Practice rewriting complex limits for easier evaluation
USEFUL FOR

Students and educators in calculus, mathematicians solving limits, and anyone looking to deepen their understanding of L'Hôpital's Rule and limit evaluation techniques.

Petrus
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Hello MHB,
I got stuck on this limit
$$\lim_{x->-\infty}x^2e^x$$

progress:
I did rewrite that as
$$\frac{e^x}{\frac{1}{x^2}}$$ and then did variabel subsitution $$t=\frac{1}{x^2}$$ but that did not work well,

Regards,
$$|\pi\rangle$$
 
Physics news on Phys.org
Try $$\frac{x^2}{e^{-x}}$$
 
ZaidAlyafey said:
Try $$\frac{x^2}{e^{-x}}$$
Hello Zaid,
Thanks once again and many thanks for the fast responed! Now I solved it with l hopitals rule!:) Cleaver!

Regards,
$$|\pi\rangle$$
 

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