Evaluate the Limit limit as x approaches 8 of xtan(1/x)

Problem

(lim_x→8)(x)*tan(1/x)

Solution

1. Identify the type of limit by substituting the value x=8 into the expression.

2. Substitute the value 8 for x in the function x*tan(1/x)

3. Evaluate the resulting expression, noting that the function is continuous at x=8 because the denominator x is non-zero and the argument of the tangent function is within its domain.

Final Answer

(lim_x→8)(x)*tan(1/x)=8*tan(1/8)

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