Continuity and DifferentiabilityHard
Question
The following function are continuous on (0, π)
Options
A.tan x
B.
C.
D.
Solution
The finction f(x) = tan x is not defined at x = 
, so f (x) not continuous on (0, π)
Since, g(x) = x sin
is continuous on (0, π) and the integral function of a continuous func tion is continuous
∴ f(x)=
dt is continuous on (0, π)
Also, f(x)
We have,
f(x) = 1
f(x) = 
2 sin 
= 1
So, f(x) is continuous at
⇒ f(x) is continuous at all other points.
Finally, f(x) =
sin(x + π)
⇒
f(x) =
and
So, f(x) is not continuous at x =
.
, so f (x) not continuous on (0, π)Since, g(x) = x sin
is continuous on (0, π) and the integral function of a continuous func tion is continuous ∴ f(x)=
dt is continuous on (0, π) Also, f(x)
We have,
f(x) = 1 f(x) = 2 sin = 1 So, f(x) is continuous at
⇒ f(x) is continuous at all other points.
Finally, f(x) =
sin(x + π)⇒
f(x) = and
So, f(x) is not continuous at x =
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