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

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

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limit as x approaches 0 of 3xcot(2x)

x \to 0 lim (3 x cot (2 x))

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to 0 lim (3 x cot (2 x))

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

= 3 \cdot x \to 0 lim (x cot (2 x))

Rewrite for L'Hopital

= 3 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( 2 x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{sec ^{2} ( 2 x ) \cdot 2})

= 3 \cdot x \to 0 lim (\frac{1}{sec ^{2} ( 2 x ) \cdot 2})

Plug in the value

x = 0

= 3 \cdot \frac{1}{sec ^{2} ( 2 \cdot 0 ) \cdot 2}

Simplify

3 \cdot \frac{1}{sec ^{2} ( 2 \cdot 0 ) \cdot 2} : \frac{3}{2}

= \frac{3}{2}

x \to 0 - lim (\frac{2}{x ^{3}})

x \to 0 lim ((1 - x^{2})^{\frac{1}{x}})

x \to 0 + lim (x sin (ln (x)))

x \to - 8 + lim (\frac{3 - 4 x}{x + 8})

x \to 0 + lim (x ln (\frac{x}{x + 1}))

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