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

Problem

(lim_x→π)(x)*sec(x)

Solution

1. Identify the function and the value that x is approaching. The function is ƒ(x)=x*sec(x) and the limit point is x=π

2. Rewrite the secant function using its reciprocal identity to make evaluation easier.

sec(x)=1/cos(x)

3. Substitute the value x=π into the expression, as both x and cos(x) are continuous at this point and the denominator is non-zero.

(lim_x→π)(x/cos(x))=π/cos(π)

4. Evaluate the trigonometric value of cos(π)

cos(π)=−1

5. Simplify the resulting fraction to find the final limit value.

π/(−1)=−π

Final Answer

(lim_x→π)(x)*sec(x)=−π

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