limit prob

[markraz]

yo yo

need help with this problem
I know the answer is -2
but Id like to see the steps

LIM 16x^2(4x^2- sqr(16x^4+1) )
x->inf

any ideas??

grazie'

 

[stapel]

LIM 16x^2(4x^2- sqr(16x^4+1) )
x->inf

any ideas??

Is the expression as follows?

. . . . .\(\displaystyle 16x^2\left(4x^2\, -\, \sqrt{16x^4\, +\, 1}\right)\)

If so, then what did you get when you followed the example(s) shown in your book (and maybe also on the board in class) with multiplying by the conjugate to make a fraction where stuff cancels?

Id like to see the steps

So would we, especially since we can't help you get un-stuck until we can see what you did that got you stuck in the first place.

 

[markraz]

Is the expression as follows?

. . . . .\(\displaystyle 16x^2\left(4x^2\, -\, \sqrt{16x^4\, +\, 1}\right)\)

If so, then what did you get when you followed the example(s) shown in your book (and maybe also on the board in class) with multiplying by the conjugate to make a fraction where stuff cancels?


So would we, especially since we can't help you get un-stuck until we can see what you did that got you stuck in the first place.

thanks for the reply. yeah your graphic shows the problem correctly. There is no example in my book. I've tried everything. How do I use a conjugate here? I thought I could only do that on a rational function. Since this has a square root doesn't that disqualify this from being a
polynomial? I don't think I can use the Theoroms of powers an polynomials on this?? not sure.

I've tried so many avenues on this problem I have exhausted my knowledge of math on this. I spent over an hour on it and I am getting nowhere. Any tip to get started would be helpful

thank you!

 

[Quaid]

need help with this problem

I know the answer is -2 but Id like to see the steps

LIM 16x^2(4x^2- sqr(16x^4+1) )
x->inf

any ideas??

Hello mark:

This is a tutoring web site; volunteers do not provide immediate step-by-step solutions here. Please be sure to check out the forum guidelines.

When taking a limit of an expression that contains a radical like this, one idea to consider right away is conjugation.

That is, rewrite the given expression in rational form, and then multiply top and bottom by the conjugate of the top.

\(\displaystyle \dfrac{16x^2(4x^2 - \sqrt{16x^4 + 1})}{1} \cdot \dfrac{16x^2(4x^2 + \sqrt{16x^4 + 1})}{16x^2(4x^2 + \sqrt{16x^4 + 1})}\)

After simplifying, you may then divide through by the highest power of x, as normally when dealing with limits at infinity.

If you need more help, please show us what you've done so far.

Cheers :cool:

 

[markraz]

Hello mark:

This is a tutoring web site; volunteers do not provide immediate step-by-step solutions here. Please be sure to check out the forum guidelines.

When taking a limit of an expression that contains a radical like this, one idea to consider right away is conjugation.

That is, rewrite the given expression in rational form, and then multiply top and bottom by the conjugate of the top.

\(\displaystyle \dfrac{16x^2(4x^2 - \sqrt{16x^4 + 1})}{1} \cdot \dfrac{16x^2(4x^2 + \sqrt{16x^4 + 1})}{16x^2(4x^2 + \sqrt{16x^4 + 1})}\)

After simplifying, you may then divide through by the highest power of x, as normally when dealing with limits at infinity.

If you need more help, please show us what you've done so far.

Cheers :cool:

sweet.. thanks I'll start with this
how do I get my next reply to look all math-like like your reply?

thanks again

 

[markraz]

Hello mark:

This is a tutoring web site; volunteers do not provide immediate step-by-step solutions here. Please be sure to check out the forum guidelines.

When taking a limit of an expression that contains a radical like this, one idea to consider right away is conjugation.

That is, rewrite the given expression in rational form, and then multiply top and bottom by the conjugate of the top.

\(\displaystyle \dfrac{16x^2(4x^2 - \sqrt{16x^4 + 1})}{1} \cdot \dfrac{16x^2(4x^2 + \sqrt{16x^4 + 1})}{16x^2(4x^2 + \sqrt{16x^4 + 1})}\)

After simplifying, you may then divide through by the highest power of x, as normally when dealing with limits at infinity.

If you need more help, please show us what you've done so far.

Cheers :cool:

does this look correct so far?
thanks

\(\displaystyle ((64x^8)-(16x^4)(16x^4+1))/(16x^2(4x^2 + \sqrt{16x^4 + 1}))\)

 

[mmm4444bot]

how do I get my next reply to look all math-like

The system that renders the pretty formatting is called LaTex. You need to learn the coding syntax, which takes some time.

If you have the time, you may google for LaTex tutorials. (Be warned that there are many variations of LaTex implemented around the Internet; not everything that you may see works at this site.)

You may right-click any LaTex expression that you see on the boards, to navigate to a pop-up displaying the code (Show Math As>>TeX commands).

At this site, LaTex code must be enclosed within [ֺtex] and [/ֺtex] tags.