Page 12 - Pra U STPM 2022 Penggal 2 - Mathematics

Mathematics Semester 2 STPM Chapter 1 Limits and Continuity
4. The function f is defined by

|5 – x| , x ≠ 5,
1 f(x) = 5 – x
0, x = 5.
lim
lim
(a) Find x → 5 – f(x) and x → 5 + f(x). Hence, determine whether f continuous at 5.
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(b) Sketch the graph of f.
5. The function f(x) is defined as follows:
3x – 1, x , 0,
f(x) = 0, x = 0,
2x + 5, x . 0.

lim
(a) Determine whether x → 0 f(x) exist. Hence, determine if f is continuous at 0.
(b) Sketch the graph of f.

6. The function f is defined by

x(x – 2), 0 < x , 2,
f(x) = 1 – 1 x, 2 < x , 3,
2
1 x – 2, 3 < x , 5.
2
Determine whether f is continuous at 2 and 3. Sketch the graph of f.

7. A function f is defined by
2
2 – x , –3 < x , 0,
2
f(x) = 2 – (x – 2) , 0 < x < 5.

(a) Show that f is discontinuous at 0.
(b) Determine whether f is continuous from the left, from the right, or neither at 0.
(c) Sketch the graph of f.
8. The function f is defined by
2 – x , 0 < x , 1,
f(x) = 3 + x
2
1 + kx , x > 1
where k  R.
lim
Given that x → 1 f(x) exists, find the value of k.
With the value of k, determine whether f is continuous at 1.

9. The function f is defined by
x – 2 , x ≠ 1, x ≠ 2,
2
f(x) = x – 3x + 2
c, x = 2.
If f is continuous at x = 2, find the value of c.

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01 STPM Math(T) T2.indd 10 28/01/2022 5:30 PM