What is the limit as x approaches (2pi)/3-of-csc(2x) ?

The limit as x approaches (2pi)/3-of-csc(2x) is (2sqrt(3))/3

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limit as x approaches (2pi)/3-of-csc(2x)

x \to \frac{2 π}{3} - lim (- csc (2 x))

\frac{2 3}{3}

Decimal

1.15470 \dots

Solution steps

x \to \frac{2 π}{3} - lim (- csc (2 x))

Plug in the value

x = \frac{2 π}{3}

= - csc (2 \cdot \frac{2 π}{3})

Simplify

- csc (2 \cdot \frac{2 π}{3}) : \frac{2 3}{3}

= \frac{2 3}{3}

x \to 0 lim (\frac{1 0 ^{x} - 4 ^{x}}{x})

x \to - 1 lim (x^{2} + 7 x + 2)

x \to 3 + lim (\frac{x - 3}{9 - x ^{2}})

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

x \to 1 lim (2 x + 5)

What is the limit as x approaches (2pi)/3-of-csc(2x) ?
The limit as x approaches (2pi)/3-of-csc(2x) is (2sqrt(3))/3