Evaluation of the Limit

To evaluate the limit, we need to substitute x=1 in the given expression and simplify it. Let's begin by writing the expression in a simpler form:

(x^3 - 3x^2)/(x^3 * (x^2 - 5x + 3))

Now, substituting x=1 in the above expression, we get:

(1^3 - 3(1^2))/(1^3 * (1^2 - 5(1) + 3))

= (1 - 3)/(-1)

= 2

Therefore, the value of the limit is 2.

Explanation

The given expression represents a rational function, where the numerator and denominator are both polynomials. To evaluate the limit, we need to substitute the given value of x in the expression and simplify it. If the simplified expression is finite, then the limit exists and is equal to the value of the expression. If the simplified expression is infinite or undefined, then the limit does not exist.

In this case, we substituted x=1 in the expression and simplified it to obtain the value 2. Therefore, the limit exists and is equal to 2.

Conclusion

To evaluate a limit, we need to substitute the given value of x in the expression and simplify it. If the simplified expression is finite, then the limit exists and is equal to the value of the expression. If the simplified expression is infinite or undefined, then the limit does not exist. In this case, we evaluated the limit of a rational function and obtained the value 2 by substituting x=1 in the expression and simplifying it.