Evaluate the Limit limit as x approaches 2 of x(x-4)

Problem

(lim_x→2)(x)*(x−4)

Solution

1. Identify the type of function. The expression x*(x−4) is a polynomial function.

2. Apply the direct substitution property for limits. Since polynomials are continuous everywhere, the limit as x approaches a value is equal to the function evaluated at that value.

3. Substitute the value x=2 into the expression.

2*(2−4)

4. Simplify the expression inside the parentheses.

2*(−2)

5. Calculate the final product.

−4

Final Answer

(lim_x→2)(x)*(x−4)=−4

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