L'hopitals Rule for Solving Limits with Complex Functions

[Sheneron]

[SOLVED] L'hopitals Derivative

Homework Statement

lim x->0 $$\frac{1-x^2-e^{-x^2}}{x^4}$$I ended up using l'hopitals rule 4 times before I got the answer. And I got an answer of -1/2. I was wondering if someone could check that to see if its right. I would post all my work but that would take a while, however, if you want to see more of my steps ill be glad to do so. I tried graphing it on my calculator, but depending where I put the parenthesis it was right or wrong. Thanks

 

[Sheneron]

My final equation looked like so...

$$\frac{16x^4e^{-x^2} - 24x^2e^{-x^2} + 16x^2e^{-x^2} - 8e^{-x^2} + 8x^2e^{-x^2} - 4e^{-x^2}}{24}$$

 

[Kurret]

You can start by replacing x^2 with y in the beginning for nicer equations. I have not been doing anything with l'hopital yet, but I used the infinite series of e^x and got the same answer as you.

 

[Sheneron]

Ok, I have another question. The derivative of $$-e^{-x^2}$$ would be $$2xe^{-x^2}$$ is that correct?

 

[Sheneron]

i just replaced it with y and that was much easier thanks

 

[exk]

yes the derivative is correct as is your solution.