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

Problem

(lim_x→8)(cos(1/x))

Solution

1. Identify the type of function. The function ƒ(x)=cos(1/x) is a composition of a trigonometric function and a rational function.

2. Check for continuity at the target value. The function 1/x is continuous at x=8 and the function cos(u) is continuous for all real numbers.

3. Apply the direct substitution property for limits of continuous functions. Since the function is continuous at x=8 the limit is equal to the value of the function at that point.

4. Substitute x=8 into the expression.

Final Answer

(lim_x→8)(cos(1/x))=cos(1/8)

Want more problems? Check here!