First slide

Continuity

Question

$The set of all points of discontinuity of the function f (x) = \frac{\tan x \log x}{1 - \cos 4 x} contains$

Moderate

A

$\{\frac{2 π}{2} : n \in Q\}$
B

$\{\frac{2 π}{2} : n \in Z\}$
C

$[- \infty, 0] \cup \{\frac{n π}{2} : n \in N\}$
D

None of these

Solution

$f (x) = \frac{\tan x \log x}{1 - \cos 4 x} 1 - \cos 4 x \neq 0 \Rightarrow \cos 4 x \neq 1 \Rightarrow 4 x \neq 2 n π \Rightarrow x \neq \frac{nπ}{2}, n \in N logx \Rightarrow x > 0 dis continuous at x \in (- \infty, 0] \cup \{\frac{nπ}{2}, n \in N\}$

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