What is the limit as θ approaches 0 of θcot(5θ) ?

The limit as θ approaches 0 of θcot(5θ) is 1/5

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limit as θ approaches 0 of θcot(5θ)

θ \to 0 lim (θ cot (5 θ))

\frac{1}{5}

Decimal Notation

0.2

Solution steps

θ \to 0 lim (θ cot (5 θ))

Rewrite for L'Hopital

= θ \to 0 lim (\frac{θ}{\frac{1}{c o t ( 5 θ )}})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{1}{sec ^{2} ( 5 θ ) \cdot 5})

= θ \to 0 lim (\frac{1}{sec ^{2} ( 5 θ ) \cdot 5})

Plug in the value

θ = 0

= \frac{1}{sec ^{2} ( 5 \cdot 0 ) \cdot 5}

sec^{2} (5 \cdot 0) \cdot 5 = 5

= \frac{1}{5}

\frac{d}{d x} (\frac{x ^{2} - 9}{x ^{2} + 9})

x^{^{''}} + x^{^{'}} + 2 x = 0

\frac{d y}{d x} = 2 y (3 - y)

y = 5 arctan (x - 1 + x^{2})

\int \frac{1}{y ^{2} - 3 y} d y

What is the limit as θ approaches 0 of θcot(5θ) ?
The limit as θ approaches 0 of θcot(5θ) is 1/5