Evaluate the Limit limit as x approaches pi of tan(x)

Problem

(lim_x→π)(tan(x))

Solution

1. Identify the function and the point of evaluation. The function is ƒ(x)=tan(x) and the limit is as x approaches π

2. Check for continuity at the given point. The function tan(x) is continuous for all x except where cos(x)=0 Since cos(π)=−1 the function is continuous at x=π

3. Apply direct substitution to evaluate the limit.

(lim_x→π)(tan(x))=tan(π)

4. Evaluate the trigonometric value. Since tan(x)=sin(x)/cos(x) we find sin(π)=0 and cos(π)=−1

tan(π)=0/(−1)=0

Final Answer

(lim_x→π)(tan(x))=0

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