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

The limit as x approaches 0 of x^3cot(x) is 0

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limit as x approaches 0 of x^3cot(x)

x \to 0 lim (x^{3} cot (x))

0

Solution steps

x \to 0 lim (x^{3} cot (x))

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 0

x \to 1 lim (\frac{1 - x ^{3}}{x - 1})

x \to - \infty lim (\frac{2 - 3 e ^{- x}}{5 e ^{- x} - 4})

x \to \infty lim (\frac{x}{e ^{- x}})

x \to 1 lim (\frac{π}{x - 1})

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

What is the limit as x approaches 0 of x^3cot(x) ?
The limit as x approaches 0 of x^3cot(x) is 0