Question

Find the limit of rational function as x->infinity and as x->-infinity
f(x)=(2x+3)/(5x+7)

Answer 1

\[\Large \lim_{x \to \pm \infty} \frac{2x + 3}{5x + 7} = \lim_{x \to \pm \infty} \frac{2 + \frac{3}{x}}{5 + \frac{7}{x}}\]

Now as x gets closer and closer to infinity, what do \(\Large \frac{3}{x}\) and \(\Large \frac{7}{x}\) tend to?

Answer 2

do they tend to get closer to 0?

Answer 3

yes

Answer 4

oh so 2/5 is left

Answer 5

yes :)

Answer 6

lol I don't know why I didn't see that

Answer 7

You can also think if it another way, if x gets really large, the +3 and +7 in the denominator start to matter very little (2*100000000 + 3 for example, the + 3 is not really that significant), so you're only interested in 2x/5x as x gets really large or small which is easy to see that it's 2/5

Answer 8

in the denominator and numerator*

Answer 9

ok got it thanks @Meepi

Answer 10

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