What is the limit as x approaches 0 of (csc(3x))/(cot(x)) ?

The limit as x approaches 0 of (csc(3x))/(cot(x)) is 1/3

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limit as x approaches 0 of (csc(3x))/(cot(x))

x \to 0 lim (\frac{csc ( 3 x )}{cot ( x )})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to 0 lim (\frac{csc ( 3 x )}{cot ( 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 (\frac{csc ( 3 x )}{cot ( x )}) = \frac{1}{3}

x \to 0 + lim (\frac{csc ( 3 x )}{cot ( x )}) = \frac{1}{3}

= \frac{1}{3}

\frac{\partial}{\partial y} (y^{6} cos (5 x))

\int_{1}^{2} \frac{7 x - 2}{3 x ^{2} - 2 x} d x

f (x) = (4 x + 3) (- x + 1), at x = 4

\frac{d}{d x} (\frac{6}{4 x})

f (x) = 7 x - x^{2}, (1, 6)

What is the limit as x approaches 0 of (csc(3x))/(cot(x)) ?
The limit as x approaches 0 of (csc(3x))/(cot(x)) is 1/3