What is the limit as x approaches pi of (tan(x))/(sin(2x)) ?

The limit as x approaches pi of (tan(x))/(sin(2x)) is 1/2

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limit as x approaches pi of (tan(x))/(sin(2x))

x \to π lim (\frac{tan ( x )}{sin ( 2 x )})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to π lim (\frac{tan ( x )}{sin ( 2 x )})

Apply L'Hopital's Rule

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

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

Plug in the value

x = π

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

Simplify

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

= \frac{1}{2}

\frac{d}{d x} (x + y + z)

\frac{d}{d x} (e^{x} + e^{x})

\frac{\partial}{\partial y} (sin (x) cos (x))

9 e^{- x}

f (x) = arctan (- 6 x)

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