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CBSE Class 12 Maths 2010 Solved Paper

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Question : 11 of 29
Marks: +1, -0
Find all points of discontinuity of f, where f is defined as following:
f (x) =
{x+3,x≤−3−2x,−3<x<36x+2,x≥3\begin{cases} x + 3, & x \le -3 \\ -2x, & -3 < x < 3 \\ 6x+2, & x \ge 3 \end{cases}
OR
Find dydx\frac{dy}{dx} , if y = (cos⁡x)x+(sin⁡x)1x(\cos x)^x + (\sin x)^{\frac{1}{x}}
Solution:  
Here, f (x) =
{x+3,x≤−3−2x,−3<x<36x+2,x≥3\begin{cases} x + 3, & x \le -3 \\ -2x, & -3 < x < 3 \\ 6x+2, & x \ge 3 \end{cases}
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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