limit as x approaches 0 of (sin^2(3x))/(4x^2)

解答

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{4 x ^{2}})

\frac{9}{4}

十进制

2.25

求解步骤

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{4 x ^{2}})

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

= \frac{1}{4} \cdot x \to 0 lim (\frac{sin ^{2} ( 3 x )}{x ^{2}})

使用洛必达法则

= \frac{1}{4} \cdot x \to 0 lim (\frac{3 sin ( 6 x )}{2 x})

使用洛必达法则

= \frac{1}{4} \cdot x \to 0 lim (\frac{18 cos ( 6 x )}{2})

代入值

x = 0

= \frac{1}{4} \cdot \frac{18 cos ( 6 \cdot 0 )}{2}

化简

\frac{1}{4} \cdot \frac{18 cos ( 6 \cdot 0 )}{2} : \frac{9}{4}

= \frac{9}{4}

x \to 0 lim (+ (x^{2} ln (x)))

x \to \frac{π}{2} - lim (ln (cos (x)))

x \to 0 lim (+ x^{x})

x \to - 2 lim (\frac{x + 2}{x})

x \to - \infty lim (3 \frac{( 3 x ^{7} - 4 x ^{5} )}{2 x ^{7} + 1})