Question

lim (x -> infinity) (11+8x)/(x^3+7x)= 0 why?

Answer 1

because the degree of the denominator is larger than the degree of the numerator
try it with x = 10^6 and you will see why this makes it true

Answer 2

so whenever the degree of the denominator is greater than the numerator, the answer is 0?

Answer 3

Because as x tends to infinity, the numerator becomes insignificant in comparison to the denominator, since the highest degree of the numerator in terms of x is 1, whilst the numerator, 3.

Answer 4

if by "whenever" you mean as x goes to infinity, the answer is yes

Answer 5

oh! so because the numerator is insignificant compared to the denominator, anything divided by infinity equals zero

Answer 6

well, the limit i mean

Answer 7

so how would it change if it was going to negative infinity?

Answer 8

still zero

Answer 9

-.000000001 vs
.000000001 still close to zero

Answer 10

thanks