Page 59 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 2 Pembezaan
26. Tentukan nilai hampir bagi setiap yang berikut. SP 2.4.8 TP5
Determine the small change for each of the following.

2 2
Diberi y = x – 2x, cari tokokan kecil dalam y apabila (a) Diberi y = 2 , cari nilai hampir bagi 2 .
2
x berubah daripada 2 kepada 2.01. Seterusnya cari (2x – 1) 2 (3.02)
nilai hampir bagi y. Given that y = (2x – 1) 2 , find the approximate value
2
2
Given y = x – 2x, find the small change in y when x changes from 2 of (3.02) 2 .
to 2.01. Then, find the approximate value of y.
Dengan bandingan: 2x – 1 = 3.02
Diberi/Given y = x – 2x By comparison 2x = 4.02
2
dy = 2x – 2 x = 2.01
dx Apabila x berubah daripada 2 kepada 2.01,
x berubah daripada 2 kepada 2.01 When x changes from 2 to 2.01, δx = 0.01
x changes from 2 to 2.01. 2
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Jadi/Then δx = 2.01 – 2 = 0.01 Dari/From y = (2x – 1) 2
δy dy dy –8
≈ Tip Penting =
δx dx δy dy dx (2x – 1) 3
dy ≈ dy
δy ≈ × δx δx dx Maka/Hence δy ≈ × δx
dx δy ≈ dy × δx dx
≈ (2x – 2) δx dx ≈ –8 δx
≈ (2(2) – 2) (0.01) (2x – 1) 3
≈ 0.02 Apabila x = 2 dan δx = 0.01
Apabila/When x = 2, y = 2 – 2(2) δy ≈ –8 (0.01) ≈ -0.00296
2
= 0 (2(2) – 1) 3 2 2
Maka, nilai hampir bagi y = y + δy Apabila/When x = 2 , y = (2(2) – 1) 2 = 9
= 0 + (0.02) 2
= 0.02 Maka, nilai hampir bagi (3.02) 2
Hence, the approximate value of y Hence, the approximate value of 2
2 (3.02) 2
= + (–0.00296) = 0.219
9
3 dy dy
(b) Diberi y = , cari . Seterusnya, cari nilai (c) Diberi y = (5x – 2) , cari dan nilai hampir bagi
3
(x + 1) 2 dx dx
1 3.05 .
3
hampir bagi .
(4.01) 2 Given y = (5x – 2) , find dy and the approximate value of 3.05 .
3
3
3
Given y = (x + 1) 2 , find dy . Then, find the approximate value dx
dx
1 Diberi/Given y = (5x – 2) 3
for .
(4.01) 2 dy = 15(5x – 2) 2
Diberi/Given y = 3 dx
(x + 1) 2 5x – 2 = 3.05
dy –6
= 5x = 5.05
dx (x + 1) 3 Apabila x berubah daripada 1 ke 1.01.
Jika/If x + 1 = 4.01 When x changes from 1 to 1.01
x = 3.01 Jadi/Then δx = 1.01 – 1 = 0.01
x berubah daripada 3 kepada 3.01 δy dy
x changes from 3 to 3.01 δx ≈ dx
Jadi/Then δx = 3.01 – 3 = 0.01 dy
δy ≈ dy δy ≈ dx × δx
δx dx 2
dy –6 ≈ 15(5x – 2) δx
δy ≈ × δx ≈ δx
dx (x + 1) 3 Apabila/When
–6
≈ (0.01) ≈ –0.00094 x = 1
(3 + 1) 3 δy ≈ 15(5(1) – 2) (0.01)
2
3
Apabila/When x = 3 , y = 16 ≈ 1.35
Maka, nilai baharu/ Hence, the new value Nilai hampir bagi 3.05 = (5 – 2) + 1.35 = 28.35
3
3
y = y + δy = 3 + (-0.00094) = 0.1866 Approximate value for
16
1
Nilai hampir bagi 1 2 = ( 0.1865) = 0.0622
Approximate value for (4.01) 3

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