Answer
$-\dfrac{25}{2}$
Work Step by Step
We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Using this and the product rule for limits, we have
$\lim\limits_{x \to -\frac{1}{2}}4x(3x+4)^2=4(-\frac{1}{2})(3(-\frac{1}{2})+4)^2=-2(-\frac{3}{2}+4)^2=-2(-\frac{3}{2}+\frac{8}{2})^2=-2(\frac{5}{2})^2=-2(\frac{25}{4})=-\frac{25}{2}.$
