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Which of the following function are continuous at x=0 ? [Note : sgn x denotes signum dunction od x.] |
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Answer» `COS((pi)/(2)sgn|X|)+sgn|x|` `"As,"sgn|x|={{:(0","x!=0),(1","x=0):}rArrcos((pi)/(2)sgn|x|)+sgn|x|=1AAx INR` `"Also,"cos((pi)/(2)sgn|x|)-sgn|x|={{:(-1","x!=0),(1","x=0):}` `"As,"sin((pi)/(2)sgn|x|)-sgn|x|={{:(1","x!=0),(0","x=0):}rArrsin((pi)/(2)sgn|x|)+sgn|x|={{:(2","x!=0),(0","x=0):}` `andsin((pi)/(2)sgn|x|)-sgn|x|=0AAx inR`. |
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