b) $\lim _{x \rightarrow \infty} \frac{12 x^{3}+7 x^{2}-4}{4 x^{4}+12 x-3}=$

Step 1 ：The limit of a rational function as x approaches infinity is determined by the highest degree of x in the numerator and the denominator. In this case, the highest degree of x in the numerator is 3 and in the denominator is 4.

Step 2 ：Therefore, the limit as x approaches infinity will be 0, because the denominator grows faster than the numerator.

Step 3 ：Final Answer: The limit as x approaches infinity of the given function is \(\boxed{0}\).