Kunci Jawaban Matematika Peminatan Sukino Kelas XII Bab 1 Limit LKS 2 B no 2

Kunci Jawaban Matematika Sukino
Matematika Peminatan Sukino Kelas XII
Limit Fungsi Aljabar dan Fungsi Trigonometri
LKS 2
Soal dan Pembahasan Matematika Sukino Peminatan
Bagian B

2. Hitung nilai setiap limit trigonometri berikut.

a.
lim x→0
sin (1 - cos x)
---------------- =
     x²

b.
lim x→0
tan (cos 4x - 1)
------------------ =
3x . sin (4/3)x

c.
lim x→0
sin[2 - 2 cos (x + 2)]
------------------------- =
x² + 4x + 4

Jawaban :

a.
lim x→0
sin (1 - cos x)
---------------- =

     x²

lim x→0
sin (1 - cos x)    (1 - cos x) 
---------------- . -------------- =
     x²                  (1- cos x)


lim x→0
sin (1 - cos x)    (1 - cos x) 
---------------- . -------------- =
  (1- cos x)              x²

lim x→0
      (1 - cos x) 
1 . -------------- =
           x²


lim x→0
 2 sin 1/2 x sin 1/2 x 
------------------------- =
      x²

2 . 1/2 . 1/2 = 1/2

----------------------------------------------------------------------------------------------------------

b.
lim x→0
tan (cos 4x - 1)
------------------ =
3x . sin (4/3)x


lim x→0
tan (cos 4x - 1)    (cos 4x - 1)
------------------ . ---------------- =
3x . sin (4/3)x      (cos 4x - 1)


lim x→0
tan (cos 4x - 1)    (cos 4x - 1)
------------------ . ---------------- =
   (cos 4x - 1)      3x . sin (4/3)x

lim x→0
(cos 4x - 1)
--------------- =
3x sin (4/3)x


lim x→0
- (1 - cos 4x)
--------------- =
3x sin (4/3)x

lim x→0
-1    2 sin 2x sin 2x
-- . ------------------ =
3    x sin (4/3)x

-1/3 . 2 . 2 . 2 . 3/4
= -2

----------------------------------------------------------------------------------------------------------


c.
lim x→0
sin[2 - 2 cos (x + 2)]
------------------------- =
x² + 4x + 4


lim x→0
sin[2 - 2 cos (x + 2)]    [2 - 2 cos (x + 2)]
------------------------- . ----------------------  =
x² + 4x + 4                   [2 - 2 cos (x + 2)]


lim x→0
sin[2 - 2 cos (x + 2)]    [2 - 2 cos (x + 2)]
------------------------- . ----------------------  =
[2 - 2 cos (x + 2)]            x² + 4x + 4

lim x→0
[2 - 2 cos (x + 2)]
---------------------- =
x² + 4x + 4

lim x→0
2 ( 1 - cos (x + 2))
---------------------- =
x² + 4x + 4

menggunakan turunan


                     sin (x+2)
2 . lim x→0 -------------=
                     2x + 4

                     sin (x+2)
2 . lim x→0 -------------=
                     2 (x + 2)

2 . 1/2 = 1

>> soal bag B no 3