Please answer this question.

Asked by dineshchem108 | 1st May, 2019, 06:34: PM

Expert Answer:

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell ax squared minus straight b comma space space minus 1 less than straight x less than 1 end cell row cell 1 over straight x comma space space straight x greater or equal than 1
fraction numerator negative 1 over denominator straight x end fraction comma space straight x less or equal than negative 1 end cell end table close
straight f left parenthesis straight x right parenthesis space is space differentiable space at space straight x equals 1
limit as straight h rightwards arrow 0 of fraction numerator straight f open parentheses 1 plus straight h close parentheses minus straight f open parentheses 1 close parentheses over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator straight f open parentheses 1 minus straight h close parentheses minus straight f open parentheses 1 close parentheses over denominator negative straight h end fraction
limit as straight h rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator 1 plus straight h end fraction end style minus begin display style 1 over 1 end style over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator straight a open parentheses 1 minus straight h close parentheses squared minus straight b minus open parentheses straight a minus straight b close parentheses over denominator negative straight h end fraction
limit as straight h rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 minus 1 minus straight h over denominator 1 plus straight h end fraction end style over denominator straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator straight a open parentheses 1 minus straight h close parentheses squared minus straight b minus open parentheses straight a minus straight b close parentheses over denominator negative straight h end fraction
limit as straight h rightwards arrow 0 of fraction numerator begin display style negative 1 end style over denominator 1 plus straight h end fraction equals limit as straight h rightwards arrow 0 of fraction numerator negative 2 straight a plus ah over denominator negative 1 end fraction
minus 1 equals 2 straight a
straight a equals fraction numerator negative 1 over denominator 2 end fraction
Also space it space is space continuous space at space straight x equals 1
limit as straight x rightwards arrow 1 of ax squared minus straight b equals straight f open parentheses 1 close parentheses equals 1
straight a minus straight b equals 1
straight b equals fraction numerator negative 3 over denominator 2 end fraction

Answered by Arun | 3rd May, 2019, 12:48: PM