Matematika

Pertanyaan

tolong jawab sama bantuin cara nya yaa
tolong jawab sama bantuin cara nya yaa

1 Jawaban

  • 1) f(x) = sin x / x = u/v
    u = sin x => u' = cos x
    v = x => v' = 1
    f'(x) = (u' v - v' u)/v^2 = (cos x . x - 1 sin x)/x^2 = (x cos x - sin x)/x^2

    g(x) = x/(sin x) = u/v
    u = x => u' = 1
    v = sin x => v' = cos x
    g'(x) = (u' v - v' u)/v^2
    = (1 sin x - cos x . x)/(sin x)^2
    = (sin x - x cos x)/(sin x)^2
    = -(x cos x - sin x)/(sin^2 x)

    f'(x)/g'(x)
    = [(x cos x - sin x)/x^2] / [-(x cos x - sin x)/(sin^2 x)]
    = - sin^2 x / x^2
    = - ((sin x)/x)^2

    2) y = 2x => m = 2
    y = x^3 - x^2 + x + 1
    y' = 3x^2 - 2x + 1
    m = y' => 3x^2 - 2x + 1 = 2
    => 3x^2 - 2x - 1 = 0
    => (3x + 1)(x - 1) = 0
    => x = -1/3 atau x = 1
    Xa + Xb = -1/3 + 1 = 2/3