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cyna · Dec 12, 2007, 12:04 AM

can someone please explain to me step by step how to solve these two problems

lim(as x goes to infinity)(X^2 +1)
(1+x+ 4x^2)

and lim(as n goes to infinity) (1-n)
(n^2 -4)

ebaines · Dec 12, 2007, 08:17 AM

A trick that often works with limit problems is to try to zero terms out. In this case, as x goes to infinity, that means divide through by a power of x, and you'll see that many of the terms fall out. I'll get you started on the first problem:

Start with:
$<br /> \displaystyle \lim_{x \to \infty} \frac {x^2+1} {1+x+4x^2}<br />$

Divide through by x^2:

$<br /> \displaystyle \lim_{x \to \infty} \frac {1+\frac 1 {x^2}} {\frac 1{x^2} +\frac 1 x +4}<br />$

Now use the fact that the limit of 1/x and 1/(x^2) as x goes to infinity is 0.

Can you take it from here?