limit as x approaches 0 of (arcsin(5x))/(sin(3x))

解答

x \to 0 lim (\frac{arcsin ( 5 x )}{sin ( 3 x )})

\frac{5}{3}

十进制

1.66666 \dots

求解步骤

x \to 0 lim (\frac{arcsin ( 5 x )}{sin ( 3 x )})

使用洛必达法则

= x \to 0 lim (\frac{\frac{5}{1 - 25 x ^{2}}}{cos ( 3 x ) \cdot 3})

代入值

x = 0

= \frac{\frac{5}{1 - 25 \cdot 0 ^{2}}}{cos ( 3 \cdot 0 ) \cdot 3}

化简

\frac{\frac{5}{1 - 25 \cdot 0 ^{2}}}{cos ( 3 \cdot 0 ) \cdot 3} : \frac{5}{3}

= \frac{5}{3}

h \to 0 lim (\frac{3 h}{h})

x \to \infty lim (5 x + 3)

x \to 5 - lim (\frac{sin ( ( x - 7 ) ( x - 5 ) )}{x - 5})

h \to 0 lim (\frac{\frac{2}{8 + h} - 8}{h})

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