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If f

Asked by sawantsb765 | 01 Jun, 2019, 20:39: PM

Expert Answer

Points space to space remember left parenthesis 1 right parenthesis space In space the space close space proximity space of space straight a space rational space number space there space is space irrational space number left parenthesis 2 right parenthesis space In space the space close space proximity space of space straight a space irrational space number space there space is space rational space number now space if space we space check space limit space at space straight x equals 0 LHL equals limit as straight x rightwards arrow 0 to the power of minus of open parentheses negative straight x close parentheses.......... from space point left parenthesis 1 right parenthesis equals negative 0 equals 0 RHL equals limit as straight x rightwards arrow 0 to the power of plus of open parentheses negative straight x close parentheses equals negative 0 equals 0.......... from space point left parenthesis 1 right parenthesis equals negative 0 equals 0 straight f left parenthesis 0 right parenthesis equals left parenthesis straight x right parenthesis equals 0 LHL equals RHL equals straight f left parenthesis 0 right parenthesis continuous space at space straight x equals 0 now space if space we space check space limit space at space straight x equals 1 LHL equals limit as straight x rightwards arrow 0 to the power of minus of open parentheses negative straight x close parentheses.......... from space point left parenthesis 1 right parenthesis equals negative 1 RHL equals limit as straight x rightwards arrow 0 to the power of plus of open parentheses negative straight x close parentheses equals negative 0 equals 0.......... from space point left parenthesis 1 right parenthesis equals negative 1 straight f left parenthesis 0 right parenthesis equals left parenthesis straight x right parenthesis equals 1 LHL equals RHL not equal to straight f left parenthesis 0 right parenthesis dicontinuous space at space straight x equals 1 similarly space at space any space irrational space number comma space for space eg space x equals square root of 2 LHL equals square root of 2.......... from space point left parenthesis 2 right parenthesis RHL equals square root of 2.......... from space point left parenthesis 2 right parenthesis straight f left parenthesis square root of 2 right parenthesis equals negative square root of 2 so space discontinuous Correct space option space left parenthesis straight b right parenthesis

Answered by Arun | 06 Jun, 2019, 09:42: AM

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