limit as x approaches 0 of (3x)/(tan(x))

解答

x \to 0 lim (\frac{3 x}{tan ( x )})

3

求解步骤

x \to 0 lim (\frac{3 x}{tan ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to 0 lim (\frac{x}{tan ( x )})

使用基本三角恒等式:

\frac{1}{tan ( x )} = cot (x)

= 3 \cdot x \to 0 lim (x cot (x))

改写以应用洛必达法则

= 3 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( x )}})

使用洛必达法则

= 3 \cdot x \to 0 lim (\frac{1}{sec ^{2} ( x )})

代入值

x = 0

= 3 \cdot \frac{1}{sec ^{2} ( 0 )}

化简

3 \cdot \frac{1}{sec ^{2} ( 0 )} : 3

= 3

y^{^{'}} - 2 x y = 2 x

x \to 1 lim (arctan (x))

y^{^{'}} - \frac{4}{x} y = \frac{1}{x ^{3}} y^{4}

\frac{d}{d x} (- 30 sin (x))

\int \frac{x}{x ^{2} + x + 2} d x