Question

y=(-x)/(x^2+1)
as x->infinity,
y=????
why

Answer 1

Since \(x^2\) dominates \(x\) the limit as \(x\) approaches infinity is 0

Answer 2

\[-\frac{x}{x^2+1}= -\frac{1}{\displaystyle\frac{x^2}{x}+\frac{1}{x}} = -\frac{1}{x+\displaystyle\frac{1}{x}}\]\[\lim_{x \to \infty}-\frac{1}{x+\displaystyle\frac{1}{x}} = 0\]

Answer 3

why divide x by x square

Answer 4

It is to demonstrate that the denominator dominates the numerator as x approaches infinity.

Answer 5

huh...??
is it we must always make the top a constant?

Answer 6

What happens to \(\displaystyle\frac{1}{x}\) for big \(x\)

Answer 7

1/0

Answer 8

i mean zero

Answer 9

As x gets very large 1/x gets very small. As you can see above, 1/x on the bottom will disappear, but you will still have -1/x which will approach 0 as x gets large.

Answer 10

so u look at things part by part? cant look at it straight?