Given the function:
[tex]g(x)=-3x^5+2x^4-5x^2+8[/tex]
Let's find the limit of the function as x approaches infinity and also as x approaches negative infinity.
We have:
[tex]\begin{gathered} \lim _{x\to\infty}-3x^5+2x^4-5x^2+8 \\ \\ \lim _{x\to\infty}g(x)=-\infty \end{gathered}[/tex]
The limit at infinity of a polynomial whose leading coefficient is negative is negative infinity.
• Also, the limit of the function at negative infinity:
[tex]\begin{gathered} g(x)=-3x^5+2x^4-5x^2+8 \\ \\ \lim _{x\to-\infty}g(x)=\infty \end{gathered}[/tex]
The limit at negtaive infinity of a polynomial whose leading coefficient is negative is infinity.
ANSWER:
[tex]\begin{gathered} \lim _{x\to\infty}g(x)=-\infty \\ \\ \lim _{x\to-\infty}g(x)=\infty \end{gathered}[/tex]
