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

Problem

(lim_x→8)(e(−8*x))*cos(x)

Solution

1. Identify the type of limit by checking if the function is continuous at the target value x=8

2. Recognize that both e(−8*x) and cos(x) are continuous functions for all real numbers.

3. Apply the direct substitution property for limits of continuous functions, which states that (lim_x→a)(ƒ(x))=ƒ(a)

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

5. Simplify the resulting expression to its exact form.

Final Answer

(lim_x→8)(e(−8*x))*cos(x)=e(−64)*cos(8)

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