What is the limit as x approaches pi/2 of ln|cos(x)| ?

The limit as x approaches pi/2 of ln|cos(x)| is -infinity

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limit as x approaches pi/2 of ln|cos(x)|

x \to \frac{π}{2} lim (ln ∣ cos (x) ∣)

- \infty

Solution steps

x \to \frac{π}{2} lim (ln ∣ cos (x) ∣)

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to \frac{π}{2} - lim (ln ∣ cos (x) ∣) = - \infty

x \to \frac{π}{2} + lim (ln ∣ cos (x) ∣) = - \infty

= - \infty

What is the limit as x approaches pi/2 of ln|cos(x)| ?
The limit as x approaches pi/2 of ln|cos(x)| is -infinity