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Asked by adjacentcalliber10 | 12 May, 2019, 15:21: PM

Expert Answer

Function space is space continuous space at space straight x equals 0 limit as straight x rightwards arrow 0 of fraction numerator acosx minus cosbx over denominator straight x squared end fraction equals straight f open parentheses 0 close parentheses limit as straight x rightwards arrow 0 of fraction numerator begin display style acosx minus cosbx end style over denominator begin display style straight x squared end style end fraction equals 4 limit as straight x rightwards arrow 0 of fraction numerator begin display style straight a open parentheses 1 minus fraction numerator straight x squared over denominator 2 factorial end fraction plus... close parentheses minus open parentheses 1 minus fraction numerator begin display style straight b squared straight x squared end style over denominator begin display style 2 factorial end style end fraction plus.. close parentheses end style over denominator begin display style straight x squared end style end fraction equals 4 limit as straight x rightwards arrow 0 of fraction numerator begin display style straight a minus 1 space plus fraction numerator begin display style straight b squared straight x squared end style over denominator begin display style 2 factorial end style end fraction minus fraction numerator ax squared over denominator 2 factorial end fraction plus.... end style over denominator begin display style straight x squared end style end fraction equals 4 limit as straight x rightwards arrow 0 of open parentheses open parentheses fraction numerator straight a minus 1 over denominator straight x squared end fraction close parentheses plus fraction numerator begin display style straight b squared minus straight a end style over denominator 2 end fraction plus... close parentheses equals 4 limit as straight x rightwards arrow 0 of open parentheses fraction numerator begin display style straight a minus 1 end style over denominator begin display style straight x squared end style end fraction close parentheses space can apostrophe straight t space be space infinity space since space there space is space straight a space finite space term space in space RHS so comma space straight a minus 1 space equals 0 straight a equals 1 also fraction numerator straight b squared minus straight a over denominator 2 end fraction equals 4 straight b equals plus-or-minus 3 ordered space pairs space left curly bracket open parentheses 1 comma 3 close parentheses space open parentheses 1 comma negative 3 close parentheses right curly bracket straight n equals 2 sum space of space straight a space equals space 2 sum space of space straight b space equals 0 total space equals space 4 option space left parenthesis straight C right parenthesis

Answered by Arun | 15 May, 2019, 10:54: AM

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