Question

Find the limit if possible.
lim x->infinity (5x^3 - 3x^2 + 10)/x^2

Answer 1

it's infinity

Answer 2

if you split it

Answer 3

Look at the highest power on top

Answer 4

then 5x -3 +10/x^2

Answer 5

it's x^3. 3>2, 2 is the highest number on the bottom

Answer 6

becaus of 5x, it is infinity

Answer 7

I mean if the polynomial on top has a higher degree, it's infinity.

Answer 8

If the polynomial on bottom has a higher degree, it's 0

Answer 9

agent's explanation is also right.

Answer 10

if the degrees are the same, then the limit is the ratio of the coefficients of the terms that have the highest degree

Answer 11

Can easily be seen if u use l'hopital's rule

Answer 12

What if the power at the bottom is higher? for example, what if its x^4 instead of x^2?

Answer 13

then it's 0.

Answer 14

basically, take the two highest powers.. x^3 approaches infinity faster than x^2, so the fraction blows up

Answer 15

if you had x^4 on the bottom, x^4 approaches infinity faster than x^3, so the fraction diminishes

Answer 16

Thanks for making it way clearer than my teacher did x.x

Answer 17

I love these moments :'D