What is the limit as x approaches 0 of sin(x)csc(6x) ?

The limit as x approaches 0 of sin(x)csc(6x) is 1/6

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limit as x approaches 0 of sin(x)csc(6x)

x \to 0 lim (sin (x) csc (6 x))

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

x \to 0 lim (sin (x) csc (6 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 (x) csc (6 x)) = \frac{1}{6}

x \to 0 + lim (sin (x) csc (6 x)) = \frac{1}{6}

= \frac{1}{6}

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

x \to - 3 lim (- 4 x)

x \to 1 lim (x + 15)

x \to 0 - lim (x + 2)

x \to a lim (0)

What is the limit as x approaches 0 of sin(x)csc(6x) ?
The limit as x approaches 0 of sin(x)csc(6x) is 1/6