What is the limit as x approaches 0 of 4xcot(x) ?

The limit as x approaches 0 of 4xcot(x) is 4

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limit as x approaches 0 of 4xcot(x)

x \to 0 lim (4 x cot (x))

4

Solution steps

x \to 0 lim (4 x cot (x))

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

= 4 \cdot x \to 0 lim (x cot (x))

Rewrite for L'Hopital

= 4 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

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

= 4 \cdot x \to 0 lim (\frac{1}{sec ^{2} ( x )})

Plug in the value

x = 0

= 4 \cdot \frac{1}{sec ^{2} ( 0 )}

Simplify

4 \cdot \frac{1}{sec ^{2} ( 0 )} : 4

= 4

\int_{0}^{1} 8 e^{2 x} d x

\frac{d}{d x} (ln (x^{2} e^{- x}))

x y - 2 y^{2} = 5, (11, 5)

\int_{1}^{2} \frac{9}{x ^{3} + 4 x} d x

What is the limit as x approaches 0 of 4xcot(x) ?
The limit as x approaches 0 of 4xcot(x) is 4