Evaluate the Limit limit as x approaches 8 of xe^(-x)

Problem

(lim_x→8)(x)*e(−x)

Solution

1. Identify the type of limit. Since the function ƒ(x)=x*e(−x) is a product of a polynomial and an exponential function, it is continuous for all real numbers.

2. Apply the direct substitution property for limits of continuous functions.

3. Substitute the value x=8 into the expression.

8*e(−8)

4. Simplify the expression by rewriting the negative exponent as a fraction.

8/(e8)

Final Answer

(lim_x→8)(x)*e(−x)=8/(e8)

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