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So, f(x) isQ. 20 Examine the differentiability of f, where f is defined byx[x]if O S x |
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Answer» Step-by-step explanation: f(1 − )= h→0 lim
(1−h)0=0 f(1 + )= h→0 lim
1+h=1 Since f is not CONTINUOUS at x=1, its also not differentiable at that point. f(2 − )= h→0 lim
(2−h)(1)=2 f(2 + )= h→0 lim
(2+h−1)2=2 f ′ (2 − )= h→0 lim
−h 2−h−2
=1 f(2 + )= h→0 lim
h 2+2h−2
=2 Hence, the function is continuous but not differentiable at x=2. |
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