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Please solve without using L'hopital rule
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Asked by g_archanasharma | 04 Mar, 2019, 11:37: AM
answered-by-expert Expert Answer
begin mathsize 12px style fraction numerator x space cos x space plus space sin x over denominator x squared plus tan x space end fraction space equals space fraction numerator cos begin display style x end style begin display style plus end style begin display style fraction numerator sin begin display style x end style over denominator x end fraction end style over denominator x plus begin display style fraction numerator tan x over denominator x end fraction end style end fraction space left parenthesis space b o t h space n u m e r a t o r space a n d space d e n o m i n a t o r space a r e space d i v i d e d space b y space x space right parenthesis limit as x rightwards arrow 0 of fraction numerator x space cos x space plus space sin space x over denominator x squared plus tan x end fraction space equals space limit as x rightwards arrow 0 of fraction numerator cos x plus fraction numerator sin begin display style x end style over denominator x end fraction over denominator x plus fraction numerator tan x over denominator x end fraction end fraction space equals space fraction numerator limit as x rightwards arrow 0 of begin display style space end style begin display style cos end style begin display style x end style begin display style space end style begin display style plus end style begin display style space end style begin display style limit as x rightwards arrow 0 of end style begin display style fraction numerator begin display style sin x end style over denominator x end fraction end style over denominator limit as x rightwards arrow 0 of begin display style space end style begin display style space end style begin display style x end style begin display style space end style begin display style plus end style begin display style space end style begin display style limit as x rightwards arrow 0 of end style begin display style space end style begin display style fraction numerator begin display style tan x end style over denominator begin display style x end style end fraction end style end fraction space equals space fraction numerator 1 plus 1 over denominator 0 plus 1 end fraction space equals space 2 end style
Answered by Thiyagarajan K | 04 Mar, 2019, 12:35: PM

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