Would you please help to answer the following question for me ?

因為是 0/0 不定式, 可用 l'Hospital's rule:

當 x → 0, (1-cos(3x))/x^2 ～ 3sin(3x)/(2x)

lim_{x→0} (3sin(3x))/(2x)

    = (3/2) lim+(x→0} sin(3x)/x

    = (3/2) (d/dx) sin(3x)|_{x=0}

    = (3/2) 3cos(3x)|_{x=0}

    = 9/2

∴ lim_{x→0} (1-cos(3x))/x^2 = 9/2

亦可不用  l'Hospital's rule 而用更基礎的公式:

(1-cos(3x))/x^2 = 2sin^2(3x/2)/x^2

    = 2 (sin(3x/2)/x)^2

因 x→0 時,

    sin(3x/2)/x = (3/2) sin(3x/2)/(3x/2) → 3/2

故得

   lim_{x→0} (1-cos(3x))/x^2 = 2(3/2)^2 = 9/2