First slide

Continuity

Question

$Let f (x) = \int_{0}^{x} t \sin \frac{1}{t} d t . Then the number of points of discontinuity of the$ $function f (x) in the open interval (0, π) is$

Moderate

A

0
B

1
C

2
D

infinite

Solution

$f (x) = x \sin \frac{1}{x} . At all points in (0, π), f^{'} (x) has a definite finite value.$
$∴ f (x) is differentiable finitely in (0, π) . As a finitely differentiable$
$function is also continuous, hence f (x) is continuous in (0, π) .$

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