Evaluate the Limit limit as x approaches 8 of sec(x)

Problem

(lim_x→8)(sec(x))

Solution

1. Identify the type of function. The function ƒ(x)=sec(x) is a trigonometric function defined as 1/cos(x)

2. Check for continuity at the target value. The function sec(x) is continuous for all x where cos(x)≠0 Since cos(8)≠0 (as 8 is not an odd multiple of π/2, the function is continuous at x=8

3. Apply the direct substitution property for limits of continuous functions.

(lim_x→8)(sec(x))=sec(8)

Final Answer

(lim_x→8)(sec(x))=sec(8)

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