To find the limit of the expression ((1-5x)^3 * (x+2)^4) / (4-5x)^7 as x approaches a certain value, we can simplify the expression and then substitute the value of x into the simplified expression.

First, let's simplify the expression:

((1-5x)^3 * (x+2)^4) / (4-5x)^7

= ((1-5x)^3 * (x+2)^4) / ((4-5x)^3 * (4-5x)^4)

= ((1-5x)^3 * (x+2)^4) / ((4-5x)^(3+4))

= ((1-5x)^3 * (x+2)^4) / (4-5x)^7

Now, let's substitute the value of x into the simplified expression. Since we don't have a specific value for x, we cannot calculate the exact limit. However, we can determine the behavior of the expression as x approaches certain values.

For example, if x approaches positive infinity, the term (1-5x)^3 will approach negative infinity, and the term (x+2)^4 will approach positive infinity. Therefore, the overall expression will approach negative infinity.

Similarly, if x approaches negative infinity, the term (1-5x)^3 will approach positive infinity, and the term (x+2)^4 will approach positive infinity. Therefore, the overall expression will approach positive infinity.

If x approaches 4/5, the denominator (4-5x) will approach zero, resulting in an undefined expression.

In summary, the limit of the expression ((1-5x)^3 * (x+2)^4) / (4-5x)^7 depends on the value of x. It approaches negative infinity as x approaches positive infinity, positive infinity as x approaches negative infinity, and is undefined when x approaches 4/5.