Why no limit

[sour hill]

the limit is technically 4x^4/37x^3 = (4/37)x

so the function approaches a line

but the line isn't horizontal - so it'll go to infinity

[stone cedar]

emm why

[sour hill]

when the biggest powers of x are the same the x's all cancel and it is just a number - which represents a horizontal line

[stone cedar]

oh okayy thnx

[sour hill]

i made a typo

i fixed it

[sour hill]

but in this case the power of x was one more on the top so there was one x left over on the top

if the power of x was 2 more it'd be x^2, and so on

and if there is any x that can't be canceled in the limit than it will either go to infinity or -infinity (for rational functions)

@stone cedar

[sour hill]

you look at which terms will grow the fastest in the numerator and denominator

and get rid of all the other terms

and then simplify

the remaining fraction

[stone cedar]

oh so for P(x)/Q(x) if the power of P(x) is greater than Q(x) then itll go infinity(or -infinity)?

[sour hill]

for rational functions, yes

[stone cedar]

okay thank you

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