Page 10 - Pra U STPM 2022 Penggal 2 - Mathematics

Mathematics Semester 2 STPM Chapter 1 Limits and Continuity

(b) y

1 4

x
f(x) = e + 3 f(x) = e – x + 4
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3

x
0 1 4 + e

Continuity at an endpoint

lim
A function f is continuous from the left at a if x → a – f(x) = f(a);
lim
a function is continuous from the right at a if x → a + f(x) = f(a).

y y

x x
0 0
a a
f is continuous from the left at a f is continuous from the right at a.

Example 6

The function f is defined by
0, x , 0,

f(x) = 1, x > 0
Determine whether f is continuous from the left at 0 and continuous from the right at 0.

lim
lim
Solution: x → 0 – f(x) = x → 0 – (0)
= 0
f(0) = 1
lim
Since x → 0 – f(x) ≠ f(0), f is not continuous from the left at 0.
lim
lim
\ x → 0 + f(x) = x → 0 + (1)
= 1
lim
Since x → 0 + f(x) = f(0) = 1, f is continuous from the right at 0.

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01 STPM Math(T) T2.indd 8 28/01/2022 5:30 PM