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

5 x^{^{''}} + 50 x - 10 = 0

\frac{\partial}{\partial y} ((2 x + 3 y)^{7})

\frac{d}{d u} (ln (u cos (v)))

\frac{d y}{d x} = x y, y (0) = 2

f (x) = 2 e^{2 x - 4} - e^{2 x - 4}

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