Question

How do you know if a limit is going to be zero when x is approaching infinity?

Answer 1

if the denominator of a fraction is increasing at a faster rate than the numerator.

Answer 2

what do you mean by increasing at a faster rate?

Answer 3

for example:
x/x^2 approaches 0 as x approaches infinity, because x approaches infinity slower than x^2

Answer 4

Example:
1/1 = 1
2/4 = 0.5
3/9 = 0.333....
4/16 = 0.25
5/25 = 0.2
6/36 = 0.166..

Answer 5

See, the bottom increases faster than the top.. The example above was for x/x^2

Answer 6

So if you keep going:
1,000,000/1,000,000,000,000 = 0.000001

Answer 7

ohhhh i see. so if it is (e^x)/(x^2), the limit would be zero?

Answer 8

no, the limit would be infinity. e^x increases faster than x^2

Answer 9

oh whoops

Answer 10

e=2.71
x=1
e^2 = something like 5 or 6
2^2 would be 4

Answer 11

So the one you gave would go off to infinity.

Answer 12

anything to the x increases faster than x to some constant power.

Answer 13

as x goes to infinity.

Answer 14

so lnx/(e^x) would have a limit of zero right

Answer 15

yes

Answer 16

ohhhh okay. thanksss