What is the limit as x approaches 0 of ln(sin^2(x)) ?

The limit as x approaches 0 of ln(sin^2(x)) is -infinity

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limit as x approaches 0 of ln(sin^2(x))

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

- \infty

Solution steps

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

Apply the Limit Chain Rule:

- \infty

= - \infty

x \to \infty lim (\frac{2}{6 x})

x \to 1 + lim (\frac{3}{x - 1})

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

x \to 0 lim (x cos (\frac{π}{x}))

x \to - \frac{π}{2} + lim (- 5 x - \frac{π}{2})

What is the limit as x approaches 0 of ln(sin^2(x)) ?
The limit as x approaches 0 of ln(sin^2(x)) is -infinity