Evaluate the Limit limit as x approaches 8 of xsin(2/x)

Problem

(lim_x→8)(x)*sin(2/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*sin(2/x)

8*sin(2/8)

3. Simplify the fraction inside the sine function.

2/8=1/4

4. Evaluate the resulting expression. Since the function is continuous at x=8 the limit is simply the value of the function at that point.

8*sin(1/4)

Final Answer

(lim_x→8)(x)*sin(2/x)=8*sin(1/4)

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