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

The limit as x approaches 0 of x*cot(x) is 1

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limit as x approaches 0 of x*cot(x)

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

1

Solution steps

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

Rewrite for L'Hopital

= 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 )})

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

Plug in the value

x = 0

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

Simplify

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

= 1

\frac{d}{d x} (x^{2} \cdot 2^{x})

2 x e^{x}

\frac{d}{d x} (e^{x^{2}} - 1)

\frac{d}{d x} (x \cdot e^{x} - 1)

\frac{\partial}{\partial x} (4 e^{x^{7} y})

What is the limit as x approaches 0 of x*cot(x) ?
The limit as x approaches 0 of x*cot(x) is 1