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

The limit as x approaches 0+of xcot(x) is 1

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limit as x approaches 0+of xcot(x)

x \to 0 + lim (x 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

x \to 0 lim (∣ x ∣)

y \to \infty lim (\frac{3 + \frac{2}{y ^{3}} - 3 y ^{4}}{9 y ^{4} - \frac{5}{y ^{2}} - 3})

x \to \infty lim (\frac{3 x + 1}{4 x ^{2} - 3 x - 7})

x \to 2 lim (x^{2} + x + 3)

x \to 4 lim (x^{2} + 3 x - 4)

What is the limit as x approaches 0+of xcot(x) ?
The limit as x approaches 0+of xcot(x) is 1