What is the limit as x approaches 0 of x[x]cot(x) ?

The limit as x approaches 0 of x[x]cot(x) is 0

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limit as x approaches 0 of x[x]cot(x)

x \to 0 lim (x [x] cot (x))

0

Solution steps

x \to 0 lim (x [x] cot (x))

Simplify

x [x] cot (x) : x^{2} cot (x)

= x \to 0 lim (x^{2} cot (x))

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 0

b \to \infty lim (e^{- b})

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

x \to - \infty lim (7^{x})

x \to π lim (\frac{cos ( 2 x )}{x})

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

What is the limit as x approaches 0 of x[x]cot(x) ?
The limit as x approaches 0 of x[x]cot(x) is 0