Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f, g and h are functions having a common domain D and h(x) ≤ f(x) ≤ g(x), x ∈ D and if 
h(x) = 
g(x) = l then 
f(x) = l . This is known as Sandwich Theorem. Using this result, compute the following limits.
(i) The value of 
A
1 0 
f(x) doesn't exist
f(x) doesn't exist
B
0 1 
f(x) doesn't exist
f(x) doesn't exist
C
1/2 1/3 
f(x) exist
f(x) exist
D
doesn/t exist (ii) 
x 4 sin (1/3 
) is – does not exist (iii) Let f(x) = x 2 
, x ≠ 0 and f(0) = 1 then – f is a continuous function
x 4 sin (1/3 ) is – does not exist (iii) Let f(x) = x 2 , x ≠ 0 and f(0) = 1 then – f is a continuous function
Text Solution
Verified by ExpertsThe correct answer is:
0
Ans.
(i)
Sol. Since 
≥ 1, so
0 ≤ 
≤ |x| , But 
|x| = 0,
Hence 0 ≤ 
≤ 
|x| = 0
∴ 
= 0
(ii)
Sol. Since – 1 ≤ sin (1/ 
) ≤ 1, so –x 4 ≤ x 4 sin (1/3 
) ≤ x 4 . But 
x 4 = 0
Hence 0 ≤ x 4 sin 1/3 
,
∴ 
x 4 sin 1/3 
= 0
(iii)
Sol.0 ≤ x 2 
= x 2 
≤ x 2 for x > 0
So, 
f(x) = 0.
Also 
f(x) = 
x 2 
= 0
Hence 
f(x) = 0
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