What you're doing is good, if you write the steps:
Hi!
I have a homework and I could not figure out 1 of 10 tasks.
I think it is really simple, if I take the "brutal" method I can see that function goes to -inf.
Even with a grapher I can see that function goes to -inf. (except for if x < 0).
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Only the first equation.
As far as I figured out I can do many things here, but the result... not so right.
First I tried to simplify, (n^4 + 1)(n^2-1).
Then tried to multiply and divide the equation with sqrt(...) + sqrt(...), tried to get a^2 - b^2 = (a-b)(a+b)
When I simplified the upper part I get n^2 - n^4, since there is a n to divide, then I can divide everything with n and get n - n^3.
Then inserting inf. I get (inf. - inf.), so no good. Tried to divide everything with the highest n, which is n^3.
Since n^3/n^3 is 1 and 1/n^3 is inf., I get -1/2= -0.5
I don't know where is the mistake!
Can someone help?
A confirmation of wolphram alpha:
lim_(n to infty) (sqrt((n^4+1)(n^ ;2-1))-sqrt(n^6-1))/(n) - Wolfram|Alpha
Yes, I saw the graph and you'll see the graph approaches to if and to if .
graph (sqrt((x^4+1)(x^ ;2-1))-sqrt(x^6-1))/(x) - Wolfram|Alpha