Page 7 - Pra U STPM 2022 Penggal 2 - Mathematics

Mathematics Semester 2 STPM Chapter 1 Limits and Continuity

Exercise 1.1

1. Find the limit of f(x) as x → 2 if f(x) is given by 1
2
2
(a) 3x + 2 (b) 2 + x (c) x – 1 (d) 1 + x – x 3
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2. Find the limit of f(x) as x → 3 if f(x) is given by
2
1 1 x – 5 x – 9
(a) (b) 2 + (c) (d)
x + 1 x x + 1 x – 3
3. Find the limit of f(x) as x → ∞ if f(x) is given by
(a) 1 + 2 – x 3 2 (b) 3x + 1
x
x
3
2
(c) x + 2x – 1 (d) x
2
2
2x + 3x + 1 3x (x – 1)
4. Evaluate
2
(a) x → 0 1 3x + x 2 2 (b) x → 1 1 x + 1 2

lim
lim
x

x + 1
2
2
lim

(c) x → 2 1 x – 4 2 (d) x → ∞ 1 x – 4x + 3 2
lim

x – 2

5x + 2
x 2
x 21
(e) x → 2 1 1 2 + 1 (f) x → ∞ 1 2x + 1 2
1 +

lim
lim
5x + 2

5. Evaluate
3
x – 1
3x + x – 2
2
lim

(a) x → 1 1 2x + 5x + 3 2 (b) x → –1 1 2x – 3x + 1 2

lim
3
3

| x – 3|
, x ≠ 3
6. A function f is defined by f(x) = x – 3
0 , x = 3
Find
(a) lim – f(x), (b) lim + f(x).
x → 3 x → 3
Hence, determine whether lim f(x) exists.
x → 3
7. The function is defined by
3x – 1, x , 0,
f(x) = 0, x = 0,
2x + 5, x . 0.
Evaluate
(a) lim f(x), (b) lim – f(x), (c) lim – f(x),
x → 2 x → 3 x → 0
(d) lim + f(x), (e) lim f(x).
x → 0 x → 0
5
01 STPM Math(T) T2.indd 5 28/01/2022 5:30 PM