What is the limit as x approaches 0 of-csc^2(x) ?

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

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limit as x approaches 0 of-csc^2(x)

x \to 0 lim (- csc^{2} (x))

- \infty

Solution steps

x \to 0 lim (- csc^{2} (x))

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

= - x \to 0 lim (csc^{2} (x))

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= - (x \to 0 lim (csc (x)))^{2}

Apply the common limit:

x \to 0 lim (csc (x)) = \infty

= - \infty^{2}

Apply Infinity Property:

\infty^{c} = \infty

= - \infty

\frac{d}{d x} (3 a^{3 x})

y = sin^{5} (3 x)

\int 2 x + 3 d x

\frac{d}{d x} (5 - 6 x)

\int x (x + 3) d x

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