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Which of the following function are continuous at x=0 ? [Note : sgn x denotes signum dunction od x.]A. `cos((pi)/(2)sgn|x|)+sgn|x|`B. `cos((pi)/(2)sgn|x|)-sgn|x|`C. `sin((pi)/(2)sgn|x|)+sgn|x|`D. `sin((pi)/(2)sgn|x|)-sgn|x|` |
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Answer» Correct Answer - A We have `cos((pi)/(2)sgn|x|)={{:(0","x!=0),(1","x=0):}` `"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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