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

Problem

(lim_x→8)(sin(x)/x)

Solution

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

2. Evaluate the numerator by substituting x=8 into the sine function, which results in sin(8)

3. Evaluate the denominator by substituting x=8 which results in 8

4. Check for indeterminacy. Since the denominator is not zero (8≠0, the function is continuous at this point, and the limit is found by direct substitution.

Final Answer

(lim_x→8)(sin(x)/x)=sin(8)/8

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