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

  • MHB
  • Thread starter Petrus
  • Start date
In summary, the limit of "x²e^x" as x approaches negative infinity is equal to zero. To solve for this limit, you can use L'Hôpital's rule or the properties of limits. The limit is equal to positive infinity, as the exponential function grows much faster than the quadratic function. By graphing the function "x²e^x", you can see that it approaches the x-axis from the positive side as x approaches negative infinity. This function can also be used to model real-world systems such as radioactive decay or population growth.
  • #1
Petrus
702
0
Hello MHB,
I got stuck on this limit
\(\displaystyle \lim_{x->-\infty}x^2e^x\)

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

Regards,
\(\displaystyle |\pi\rangle\)
 
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  • #2
Try \(\displaystyle \frac{x^2}{e^{-x}}\)
 
  • #3
ZaidAlyafey said:
Try \(\displaystyle \frac{x^2}{e^{-x}}\)
Hello Zaid,
Thanks once again and many thanks for the fast responed! Now I solved it with l hopitals rule!:) Cleaver!

Regards,
\(\displaystyle |\pi\rangle\)
 

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

What is the limit of "x²e^x" as x approaches negative infinity?

The limit of "x²e^x" as x approaches negative infinity is equal to zero.

How do you solve for the limit of "x²e^x" as x approaches negative infinity?

To solve for the limit of "x²e^x" as x approaches negative infinity, you can use L'Hôpital's rule or the properties of limits to simplify the expression and evaluate the limit.

Is the limit of "x²e^x" as x approaches negative infinity equal to positive or negative infinity?

The limit of "x²e^x" as x approaches negative infinity is equal to positive infinity, as the exponential function grows much faster than the quadratic function as x becomes more negative.

Can you graph the function "x²e^x" to better understand its behavior at negative infinity?

Yes, by graphing the function "x²e^x", you can see that it approaches the x-axis (y=0) from the positive side as x approaches negative infinity.

Are there any real-world applications of "x²e^x" and its limit at negative infinity?

Yes, the function "x²e^x" and its limit at negative infinity can be used to model the growth or decay of certain physical systems, such as radioactive decay or population growth in limited resources.

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