Question

1. $f(x) = x^3 + 4x^2 - 3$

$limlimits_{x \to -\infty} f(x) = \infty$
$limlimits_{x \to \infty} f(x) = -\infty$

Explanation:

Step1: Identify leading term

The leading term of $f(x)$ is $x^3$.

Step2: Analyze limit as $x\to-\infty$

For $x\to-\infty$, $x^3\to-\infty$, lower degree terms become negligible:
$\lim_{x\to-\infty} (x^3 + 4x^2 - 3) = -\infty$

Step3: Analyze limit as $x\to\infty$

For $x\to\infty$, $x^3\to\infty$, lower degree terms become negligible:
$\lim_{x\to\infty} (x^3 + 4x^2 - 3) = \infty$

Answer:

$\lim_{x\to-\infty} f(x) = -\infty$
$\lim_{x\to\infty} f(x) = \infty$