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Alfi asked in Sains & MatematikaMatematika · 9 years ago

Lim x->45 (cos2x)/sin x-cosx?

2 Answers

Rating
  • Anonymous
    9 years ago
    Favorite Answer

    k = (cos 2x)/(sin x - cos x)

    lim x → ¼ π

    misalkan x + y = ¼ π

    k = (cos 2(¼ π - y))/(sin (¼ π - y) - cos (¼ π - y))

    lim y → 0

    k = (cos (½ π - 2y))/(√2 cos (¼ π - y - ¾ π))

    lim y → 0

    k = (sin 2y)/(√2 cos (½ π + y))

    lim y → 0

    k = -(sin 2y)/(√2 sin y)

    lim y → 0

    k = -(sin 2y)/(2y) * (y/sin y) * √2

    lim y → 0

    k = -1 * 1 * √2

    k = -√2

  • Adhel
    Lv 7
    9 years ago

    aku anggap 45 itu 45 derajat bisa juga ditulis π/4

    maka

    lim x→π/4 (cos 2x )/(sin x - cos x)

    lim x→π/4 (cos²x - sin²x)/(sin x - cos x) faktorkan

    lim x→π/4 ((cos x+sin x)(cos x-sin x))/(sin x - cos x) corat coret

    lim x→π/4 (cos x+sin x)/-1

    (2/√2)/(-1) = -√2

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