Algebraically Find limit to infinity

[KJF]

lim as x -> infinity (5x^4+x)^(1/2) / (x+1)(3x-2)

so far I have
lim as x approaches infinity = (5+(x/x^4))^1/2 / (x-(1/x))(3-(2/x))
next step I am not sure of:
lim as x approaches infinity (5+ (1/x^3))^1/2 / lim as x approaches infinity (x-(1/x)) lim as x approaches infinity (3-(2/x))?



Also: any advice in what software (Latex) etc. to use to make this problem look more clear?
Many thanks for any help

 

[lookagain]

lim as x -> infinity (5x^4+x)^(1/2) / (x+1)(3x-2) \(\displaystyle \ \ \ \) <---- Grouping symbols are missing around the denominator as a whole *

so far I have



lim as x approaches infinity = (5+(x/x^4))^1/2 / (x-(1/x))(3-(2/x)) \(\displaystyle \ \ \) See * above. A sign changed (is wrong) in a factor. An "x" should be a "1."

Parentheses are missing from around the fractional exponent.

lim ( x --> oo) {[5 + x/(x^4)]^(1/2)}/[(1 + 1/x)(3 - 2/x)]



lim ( x --> oo) {[5 + 1/(x^3)]^(1/2)}/[(1 + 1/x)(3 - 2/x)]



{[5 + 0]^(1/2)}/[(1 + 0)(3 - 0)]




\(\displaystyle \dfrac{\sqrt{5}}{3}\)

 

[michala20]

lim as x -> infinity (5x^4+x)^(1/2) / (x+1)(3x-2)

so far I have
lim as x approaches infinity = (5+(x/x^4))^1/2 / (x-(1/x))(3-(2/x))
next step I am not sure of:
lim as x approaches infinity (5+ (1/x^3))^1/2 / lim as x approaches infinity (x-(1/x)) lim as x approaches infinity (3-(2/x))?



Also: any advice in what software (Latex) etc. to use to make this problem look more clear?
Many thanks for any help

should get to the form: (5+1/x^3)^1/2 / (3-2/x)(1/x+1)
From here is should be simple.

 

[DrPhil]

LaTeX

lim as x -> infinity (5x^4+x)^(1/2) / (x+1)(3x-2)
Also: any advice in what software (Latex) etc. to use to make this problem look more clear?
Many thanks for any help

Thids board has a very good LaTeX interface, activated by enclosing each line of LaTeX coding in a block delimited by tags enclosed in [..], the tags being tex and /tex. You can look at the code for any equation you find on the board by right-clicking on it and then clicking Show Math As > TeX Commands. I think that is the best way to learn the commands.

For instance,

\(\displaystyle \displaystyle \lim_{x \to \infty} \left[ \dfrac{(5x^4 + x)^{1/2}}{(x + 1)(3x - 2)} \right] =\lim_{x \to \infty} \left( \dfrac{\sqrt{5}x^2}{3x^2} \right) = \dfrac{\sqrt{5}}{3}\)

If you don't already know LaTeX, a good reference is
http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols

Also
http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Commands

 

[lookagain]

should get to the form: (5 + 1/x^3)^(1/2)/[(3 - 2/x)(1/x + 1)]
From here [it] should be simple.

michala20, you must include grouping symbols for that fractional exponent and also for around that entire denominator.

I put them in bold. Also, it is easier to read if you would space the characters out horizontally as I have done as well.

(I don't know why you rearranged the order of the binomial factors in the denominator.)

 

[KJF]

Thanks

Thank you, Lookagain; I guess I had gotten pretty far, but didn't trust myself enough to plug in the 0's. I was lazy with the parenthesis, I will focus better in future. Thanks DrPhil, I know this wasn't the correct area of the forum to ask for that advice, so I appreciate your help.