Limit of a product is the product of the limits - when? The limit of the product of two functions should be equal to the product of the limits:
$$\lim_{x\to\infty}f(x)g(x) = \lim_{x\to\infty}f(x) \lim_{x\to\infty}g(x)$$
Now, the limit of $\frac{(x-1)3}{4x}$ = $\frac{3}{4}$
But the limit of $\frac{x-1}{4}$ = $\infty$ and the limit of $\frac{3}{x}$ = 0
How is this? Thanks!

The two expressions are equal when both of the limits on the right side exist and are finite numbers.
Likewise $\displaystyle \lim_{x\to a}\frac{f(x)}{g(x)} = \frac{\lim_{x\to a} f(x)}{\lim_{x\to b} g(x)}$ if the limits in the numerator and denominator exist and are finite numbers and the limit in the denominator is not $0$.  But it is crucially important to consider limits of the form on the left side in the case where the two limits on the right side are both $0$, because that is what derivatives are.
