Page 16 - Pra U STPM 2022 Penggal 2 - Mathematics

Mathematics Semester 2 STPM Chapter 1 Limits and Continuity

STPM PRACTICE 1

1
1. Evaluate 2 1 x + 1 2
x – 1
lim
lim
(a) x → –3 √x + 4 – 1 (b) x → 1 4e x – 1 – 1
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x + 3
2e 1 x + 1 2 – 1
2. (a) State the three conditions in which function f, f(x) is not continuous at point x = c.
(b) A function g is defined by
8 – x , x , 6
7 –
g(x) =  x
2
x – 2x – 6 , x > 6 where k ≠ 0
kx
Determine the set of values of k such that g is not continuous at point x = 6.

3. The function f is defined by
x – a, x < –3,
2
f(x) = bx + 2, –3 , x < 1,
3x + 2, x . 1.
lim
lim
Determine the value of a and the value of b if x → –3 f(x) and x → 1 f(x) exist.
4. The function f is defined by
f(x) = x + 2, –2 < x , 2,
|x| – 2, otherwise.

lim
lim
lim
lim
(a) Find x → –2 – f(x), x → –2 + f(x), x → 2 – f(x) and x → 2 + f(x).
(b) Determine whether f is continuous at –2 and 2.
5. Evaluate
x – 10
lim
lim
(a) x → 3 8 (x – 3) (b) x → 10 √ 7 – √ x – 3
3
x – 27
6. The function f is defined by
x – 4 , x , 2,
2
x – 2
2
f(x) = a – 2, x = 2
|2 – x| + b , x . 2
x – 2
Where a and b are constants.
lim
(a) If x → 2 f(x) exists, find the value of b.
(b) If f(x) is continuous at x = 2, determine the values of a.

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01 STPM Math(T) T2.indd 14 28/01/2022 5:30 PM