Find Limit

[Thanh Hai Dang]

Using L'Hopital rule to find the limit:
[MATH]\lim_{x\rightarrow 0}{\frac{x^2e^x - ln(1+x^2)-arcsin(x^3)}{xsinx -x^2}}[/MATH]
Thank you!

 

[pka]

Using L'Hopital rule to find the limit:
[MATH]\lim_{x\rightarrow 0}{\frac{x^2e^x - ln(1+x^2)-arcsin(x^3)}{xsinx -x^2}}[/MATH]

Do you plan to show what you have done? We need to see where you are having trouble.

 

[Thanh Hai Dang]

Hi pka when i found differential of numerator and denominator i obtained the bulky expressions. So, I can't continue to find differential. Is there a way to simplify the expression in the numerator or denominator to use L'Hopital Rule? Thank you!

P/s: Sorry because of my poor English.

 

[Dr.Peterson]

Hi pka when i found differential of numerator and denominator i obtained the bulky expressions. So, I can't continue to find differential. Is there a way to simplify the expression in the numerator or denominator to use L'Hopital Rule? Thank you!

P/s: Sorry because of my poor English.

Please show your "bulky expressions" for the derivatives, so we can see if they are correct. If they are, then it shouldn't matter that they are "bulky" (I like that term), as long as you are able to substitute x=0 -- unless the result is still indeterminate. Is that what happened?

 

[Thanh Hai Dang]

Please show your "bulky expressions" for the derivatives, so we can see if they are correct. If they are, then it shouldn't matter that they are "bulky" (I like that term), as long as you are able to substitute x=0 -- unless the result is still indeterminate. Is that what happened?

Hi Dr.Peterson, this is my expressions. I can't continue to find differential, although the limit still in 0/0 form.
[MATH] \lim_{x\rightarrow 0}\frac{(x^2+2x)e^x-\frac{2x}{1+x^2}-\frac{3x^2}{\sqrt{1-x^6}}}{sinx+xcosx-2x} [/MATH]how can I simplify the limit before using L'Hopital Rule? Or I must continue to find derivatives of this bulky expressions?
thank you!

 

[Steven G]

You multiply by numerator and denominator by the lcm( 1+x², sqrt(1-x⁶)).

A prerequisite for calculus 1 is algebra and there is a reason for that.

 

[pka]

Hi pka when i found differential of numerator and denominator i obtained the bulky expressions. So, I can't continue to find differential. Is there a way to simplify the expression in the numerator or denominator to use L'Hopital Rule?

This is a ridiculously complicated problem. Look at this link .
I see no redeeming purpose in this question!

 

[Thanh Hai Dang]

This is a ridiculously complicated problem. Look at this link .
I see no redeeming purpose in this question!

sr Pka, I think you have a little bit of confusion. In the numerator, we have [MATH]x^2e^x [/MATH] instead of [MATH] xe^x[/MATH].
in this link.

 

[Thanh Hai Dang]

You multiply by numerator and denominator by the lcm( 1+x², sqrt(1-x⁶)).

A prerequisite for calculus 1 is algebra and there is a reason for that.

After multiply by numerator and denominator by the lcm( 1+x², sqrt(1-x⁶)), i will receive a more bulky expression, won't I?
Can you show the limit after doing that?
Thank you!

 

[Steven G]

No, you try to do the multiplication, show us your work and if there is an error then we will point it out. On the forum we do not do any work for students as we want to help them.

You can always take the derivative of the numerator as it is which may not be a bad idea. Please give it a try maybe you'll like it.