What is the limit as x approaches 0 of sin(x)cot(2x) ?

The limit as x approaches 0 of sin(x)cot(2x) is 1/2

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limit as x approaches 0 of sin(x)cot(2x)

x \to 0 lim (sin (x) cot (2 x))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (sin (x) cot (2 x))

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{2}

x \to 3 lim (x^{2} - 3 x + 7)

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

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

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

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

What is the limit as x approaches 0 of sin(x)cot(2x) ?
The limit as x approaches 0 of sin(x)cot(2x) is 1/2