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

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})

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}

ma c l a u r in 9 e^{- x}

\int \frac{1}{( 16 - x ^{2} ) ^{\frac{3}{2}}} d x

d er i v a t i v e f (x) = 3 csc (4 x)

x y^{^{'}} + 4 y = 9 x^{5} + 2 x^{3}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 t}

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