(Section 3.7) Let $f(x) = x^2 + x^{-1} + e^{2x} + e^{-2x}$.
What is the behavior of each term as $x \rightarrow \infty$?
Type "inf" if the answer is $\infty$ or "-inf" if the answer is $-\infty$.
As $x \rightarrow \infty$, $x^2 \rightarrow \infty$
As $x \rightarrow \infty$, $x^{-1} \rightarrow \infty$
As $x \rightarrow \infty$, $e^{2x} \rightarrow \infty$
As $x \rightarrow \infty$, $e^{-2x} \rightarrow \infty$
What is the behavior of each term as $x \rightarrow -\infty$?
Type "inf" if the answer is $\infty$ or "-inf" if the answer is $-\infty$.
As $x \rightarrow -\infty$, $x^2 \rightarrow \infty$
As $x \rightarrow -\infty$, $x^{-1} \rightarrow -\infty$
As $x \rightarrow -\infty$, $e^{2x} \rightarrow -\infty$
As $x \rightarrow -\infty$, $e^{-2x} \rightarrow \infty$
What is the leading behavior of $f(x)$ at $\infty$?
What is the leading behavior of $f(x)$ at $-\infty$?
