Question

lim( x^4-5x^2+1) as x goes to infinity = infinity. can someone explain?

Answer 1

correction: as x goes to negative infinity

Answer 2

why does infinity-infinity+1= infinity?

Answer 3

No its the exponents that indicate the infinity

Answer 4

isolate leading factor

lim x^(4)
x-> infinity

thus

= infinity

Answer 5

infinity^4 - infinity^2 = infinity
you ignore the 1 and 5 because those are so small compare to infinity and do not have as big of effect as the exponents

Answer 6

if you put an infinitely large number into x^(4) it is always going to pump out a positive output that is infinitly large, therefore it equals infinity

Answer 7

We isolate the leading factor because 5x^(4) and +1 is like a sand grain in comparison to a desert that is x^(4) interms of what it out puts

Answer 8

oh okay yeah you factor out an x^4, thanks :)

Answer 9

no factoring isolating read my explanation

Answer 10

why we only take the leading term into account

Answer 11

we only take it into account because it dictates what the functions out put is going to be

Answer 12

so we only take into account the term with the highest exponent?

Answer 13

yes because x^(4) will out put a higher value than 5x^(2) thus 5x^(2) doesn't matter when inputing an infinitly large number does it. Same goes if it was 5x^(2)

Answer 14

okay that makes it a lot easier to understand, thanks

Answer 15

when looking at limits you are only looking at where the graph is going