What is the limit as x approaches 0 of 5xcot(2x) ?

The limit as x approaches 0 of 5xcot(2x) is 5/2

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limit as x approaches 0 of 5xcot(2x)

x \to 0 lim (5 x cot (2 x))

\frac{5}{2}

Decimal

2.5

Solution steps

x \to 0 lim (5 x cot (2 x))

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

= 5 \cdot x \to 0 lim (x cot (2 x))

Rewrite for L'Hopital

= 5 \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})

= 5 \cdot x \to 0 lim (\frac{1}{sec ^{2} ( 2 x ) \cdot 2})

Plug in the value

x = 0

= 5 \cdot \frac{1}{sec ^{2} ( 2 \cdot 0 ) \cdot 2}

Simplify

5 \cdot \frac{1}{sec ^{2} ( 2 \cdot 0 ) \cdot 2} : \frac{5}{2}

= \frac{5}{2}

\int \frac{1}{s ^{2} + 6 s + 11} d s

y = x^{2} + x + 8

\frac{d}{d x} (- \frac{3}{2} x^{5} + \frac{2}{5} x^{3} - \frac{1}{6} x^{2} - 4 x)

y = ln (\frac{x}{5 - x})

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

What is the limit as x approaches 0 of 5xcot(2x) ?
The limit as x approaches 0 of 5xcot(2x) is 5/2