Find all points of discontinuity of f, where f is defined ...

CBSE Class 12 Maths 2010 Solved Paper

Question : 11 of 29

Marks: +1, -0

Find all points of discontinuity of f, where f is defined as following:
f (x) =

\{\table \\x\\ + 3 , x ≤ - 3 ; -2x , - 3 < x < 3; 6x+2 , x ≥ 3

OR
Find

{dy}/{dx}

, if y =

(cosx)^x + (sinx)^{1/x}

Solution:

Here, f (x) =

\{\table \x\ + 3 , x ≤ - 3 ;-2x , - 3 < x < 3; 6x+2 , x ≥ 3

The function is defined on all the points and hence continuous possible points ofdiscontinuity are 3 and -3 . We need to check the continuity of the function at twopoints x = 3 and x = -3.
Case 1: For x = -3, f(-3) = -(-3) + 3 = 6
LHL = lim

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