Question

Can you solve this problem this way?

Lim x--> + infinity (3x^4 + 5x +1)/(1+x^2)
= Lim x--> + infinity (3 + 5/x^3 +1/x^4)/(1/x^4 + 1/x^2) = 3

Answer 1

No you cannot. The denominator becomes 0 as x-> +infinity and f(x) becomes undefined.

Factor x^2 out of the numerator and denominator. They will cancel out. Then try x->+infinity.

Answer 2

But wouldn't it just be 3/0+ = + infinity?

Answer 3

Because it's approaching 0, but not exactly 0 right?

Answer 4

But in the problem you had the limit as 3. But the limit is +infinity.

Answer 5

Sorry I meant to write + infinity!

Answer 6

(3x^4 + 5x +1)/(1+x^2) = x^2(3x^2 + 5/x + 1/x^2) / { x^2(1 + 1/x^2) } =
(3x^2 + 5/x + 1/x^2) / (1 + 1/x^2) As x->+infinity:
| | |
0 0 0
So you are left with just 3x^2 that goes to +infinity as x goes to +infinity

Answer 7

Thank you!

Answer 8

you are welcome.