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) ∣)

cos (x)

is positive when

x \to \frac{π}{2} -

. Therefore

∣ cos (x) ∣ = cos (x)

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply the Limit Chain Rule:

- \infty

= - (- \infty)

Simplify

= \infty

x \to 0 lim (x^{3} sin (\frac{2}{x}))

x \to 5 lim (\frac{5 - x}{5 - x})

x \to - 2 - lim (x + 6)

x \to 0 + lim (\frac{x + 5}{x})

x \to 5 lim (\frac{\frac{1}{9 x + 9} - \frac{1}{54}}{\frac{1}{9 x + 10} - \frac{1}{55}})

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