What is the limit as x approaches 0 of sin(2x)csc(3x) ?

The limit as x approaches 0 of sin(2x)csc(3x) is 2/3

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limit as x approaches 0 of sin(2x)csc(3x)

x \to 0 lim (sin (2 x) csc (3 x))

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

x \to 0 lim (sin (2 x) csc (3 x))

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

then

x \to a lim f (x) = L

x \to 0 - lim (sin (2 x) csc (3 x)) = \frac{2}{3}

x \to 0 + lim (sin (2 x) csc (3 x)) = \frac{2}{3}

= \frac{2}{3}

What is the limit as x approaches 0 of sin(2x)csc(3x) ?
The limit as x approaches 0 of sin(2x)csc(3x) is 2/3