Fundamental Theorem of Algebra Limit Proof

[harrietstowe]

Homework Statement

prove that the limit of a_nxⁿ + a_n-1x^n-1 + ... + a₁x¹ + a₀ as x goes to infinity equals infinity

** I forgot to mention that n is an odd number and this is for n>0 otherwise yes your counter example would be correct**
Thanks for the quick responses by the way
Otherwise, that is all the information given

Homework Equations

The Attempt at a Solution

I tried pulling xⁿ out and factoring and I see how some of the terms inside the parenthesis would go to zero but I was ending up with infinity * 0 which doesn't exist.
Thank You

Homework Statement

Homework Equations

The Attempt at a Solution

 

[fzero]

I tried pulling xⁿ out and factoring and I see how some of the terms inside the parenthesis would go to zero but I was ending up with infinity * 0 which doesn't exist.

You might want to post your result. The leading term of your expression (inside the parentheses) should be finite.

 

[Mark44]

Homework Statement

prove that the limit of a_nxⁿ + a_n-1x^n-1 + ... + a₁x¹ + a₀ as x goes to infinity equals infinity

As stated, this is not true. Here's a counterexample:
$$\lim_{x \to \infty} -2x^2 + 3x + 5 = -\infty$$

Have you omitted some of the information in this problem?

Homework Equations

The Attempt at a Solution

I tried pulling xⁿ out and factoring and I see how some of the terms inside the parenthesis would go to zero but I was ending up with infinity * 0 which doesn't exist.
Thank You

 

[Mark44]

Here's another counterexample, with n > 0 and n odd.

$$\lim_{x \to \infty} -2x^3 + 3x + 5 = -\infty$$

The behavior for large and positive x is controlled by the sign of a_n, the coefficient of the highest-degree term.