Matematika

Pertanyaan

1. Lim x->0 (10x-3sinx)/x =
2.Lim x->0 (1-cosx)/x =
3.Lim x->0 (sin²x)/(3x²) =

tolong bantu jawab yaa
1. Lim x->0 (10x-3sinx)/x = 2.Lim x->0 (1-cosx)/x = 3.Lim x->0 (sin²x)/(3x²) = tolong bantu jawab yaa

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1 Jawaban

  • 3) Lim (10x - 3 sin x)/x
    x => 0

    Lim (10x)/x - 3 (sin x)/x
    x=>0

    = 10 - 3(1)

    = 7

    4) Lim (1 - cos x)/x
    x => 0

    Lim (1 - cos x)/x . (1 + cos x)/(1 + cos x)
    x=>0

    Lim (1 - cos^2 x) / x(1 + cos x)
    x=>0

    Lim sin^2 x / x(1 + cos x)
    x=>0

    Lim (sin x)/x . (sin x)/(1 + cos x)
    x=>0

    = 1 . (sin 0)/(1 + cos 0)

    = 1 . 0/(1 + 1)

    = 0

    5) Lim (sin^2 x)/(3x^2)
    x => 0

    Lim (sin x)/(3x) . (sin x)/x
    x=>0

    = 1/3 . 1/1

    = 1/3

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