Matematika

Pertanyaan

Tolong yg ngerti bantu jwb ya,thx:)
Tolong yg ngerti bantu jwb ya,thx:)

1 Jawaban

  • Limit trigonometri

    a) lim(x->π)  sinx/(1 - cos x)
    sub x = π
    = sin π/ ( 1 - cos π)
    = 0/ (1 - (-1)
    = 0/2
    = 0

    b.lim(x - π/4)  1 + tan x / csc x + 2
    sub x = π/4
    = (1 + tan π/4) / (1/sin π/4  + 2)
    = (1 + 1) / (√2 + 2)
    = 2/ (√2+2)
    = 2(√2 -2) / (2 - 4) = 2 (√2 - 2)/(-2)
    = - (√2 -2)
    = 2 - √2

    c. lim (x->0) (1 - sin x) / cos² x
    x= 0
    = (1 - sin 0)/(cos 0)²
    = (1 - 0)/ (1)²
    = 1

    d. lim(x->0)  (1 - cos x)/(sin² x)
    x= 0  --> bntuk 0/0
    lim(x->0)  (2 sin² 1/2 x ) / sin² x
     = 2 (1/2)² /(1)
    = 1/2