Published by:
CGP EDU Academic Team
Published on: August 13, 2026
f(x) = 
where [.] represents the greatest integer function.
Find A and B such that f(x) is continuous at x = 0.
Text Solution
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CHECK THE SOLUTION.
Sol. 
f(x) = 
=
= 
For this limit to exist, we must have A + 3 = 0 and that case, 
f(x) = – 
Now, 
f(x) = 
B tan 
= B tan 
= 
B
Also f(0) = B tan 
= B 
Thus, if f(x) is continuous at x = 0, then
A + 3 = 0 and 
f(x) = 
f(x) = f(0)
⇒ A + 3 = 0 and – 
= B 
∴ A = –3 and B = – 
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