limit as x approaches pi/4 of (sin(2x))/(sin(x)tan(x))

解答

x \to \frac{π}{4} lim (\frac{sin ( 2 x )}{sin ( x ) tan ( x )})

2

十进制

1.41421 \dots

求解步骤

x \to \frac{π}{4} lim (\frac{sin ( 2 x )}{sin ( x ) tan ( x )})

代入值

x = \frac{π}{4}

= \frac{sin ( 2 \cdot \frac{π}{4} )}{sin ( \frac{π}{4} ) tan ( \frac{π}{4} )}

化简

\frac{sin ( 2 \cdot \frac{π}{4} )}{sin ( \frac{π}{4} ) tan ( \frac{π}{4} )} : 2

= 2

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