Page 41 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 2 Pembezaan
3. Selesaikan soalan graf fungsi f(x) yang berikut. SP 2.1.1 TP5
Solve the following questions of the function graph f(x).

y (a) y
4
y = f(x) y = f(x)
3 3
2

–2 0 5 6 x –2 0 3 4 x
–1 –1

Rajah menunjukkan sebahagian graf fungsi f(x) Rajah menunjukkan sebahagian graf fungsi f(x)
untuk –2 < x < 6. Berdasarkan kepada graf, untuk –2 < x < 4. Berdasarkan kepada graf,
dx Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
The diagram shows a part of the function f(x) for –2 < x < 6. The diagram shows a part of the function f(x) for –2 < x < 4.
Based on the graph, Based on the graph,
(i) cari/find had/lim f(x) (i) cari / find f(–2)
x → –2
(ii) tentukan sama ada had f(x) wujud atau (ii) tentukan sama ada had f(x) wujud atau
x → 0
tidak. Jelaskan. x → 0 tidak. Jelaskan.
determine whether lim f(x) exists or not. Explain. determine whether lim f(x) exists or not. Explain.
x → 0 x→0
(i) had/lim f(x) = 4 (i) f(–2) tidak tertakrif, maka tidak ada nilai.
x → -2 f(–2) is not defined, hence there is no value.

(ii) Kiri/Left: had/lim f(x) = –1 (ii) Kiri/Left: had/lim f(x) = 3
x → 0
x → 0
Kanan/Right: had/lim f(x) = 2 Kanan/Right: had/lim f(x) = 3
x → 0
x → 0
Nilai tidak sama, nilai had f(x) tidak wujud. Nilai sama, nilai had f(x) wujud.
x → 0 x → 0
The values are not the same, lim f(x) does not exist.
x → 0 Same value, lim f(x) exists.
x → 0

4. Cari dy dengan menggunakan prinsip pertama bagi setiap fungsi y = f(x) yang berikut. SP 2.1.2 TP3
dx
dy
Find dx by using the first principles for each of the following functions y = f(x).

–1
(a) y =
y = 2x – 1 x
y + δy = 2(x + δx) – 1 Tip Penting y + δy = –1
2x – 1 + δy = 2x + 2δx – 1 Gunakan/ Use (x + δx)
(y + δy)(x + δx) = –1
δy = 2δx dy = had/lim δy yx + yδx + xδy + δx.δy = –1

dx
δx → 0 δx
δy = 2 xδy + δx.δy = –yδx
δx
Maka/Hence dy = had/lim δy (x + δx)δy = –yδx

δx → 0 δx δy = 1
= had/lim 2 δx x(x + δx)
δx → 0 dy had/lim δy

= 2 Maka/Hence dx = δx → 0 δx
= had/lim 1
δx → 0 x(x + δx)
= 1
x(x)

= 1
x 2

© Penerbitan Pelangi Sdn. Bhd. 20

02 Hybrid PBD Mate Tamb Tg5.indd 20 09/11/2021 9:24 AM