L'Hopital question help!????????????????

$begin inline style italic lim with x rightwards arrow 0 below end style fraction numerator italic sin open parentheses x close parentheses open parentheses 1 minus x close parentheses over denominator x end fraction$

$fraction numerator italic sin open parentheses 0 close parentheses open parentheses 1 minus 0 close parentheses over denominator 0 end fraction$ (Substitute in the above function)

$fraction numerator open parentheses 0 close parentheses open parentheses 1 close parentheses over denominator 0 end fraction$

$fraction numerator open parentheses 0 close parentheses over denominator 0 end fraction$

L'Hospital's rule : $i f italic lim with x rightwards arrow 0 below fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equal fraction numerator f open parentheses 0 close parentheses over denominator g open parentheses 0 close parentheses end fraction equal 0 over 0 o r space fraction numerator plus-minus infinity over denominator plus-minus infinity end fraction space t h e n space begin inline style italic lim with x rightwards arrow 0 below end style fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction space equal begin inline style italic lim with x rightwards arrow 0 below end style fraction numerator f apostrophe open parentheses x close parentheses over denominator g apostrophe open parentheses x close parentheses end fraction$

$italic lim with x rightwards arrow 0 below fraction numerator open parentheses italic sin open parentheses x close parentheses close parentheses open parentheses 1 minus x close parentheses over denominator x end fraction equal italic lim with x rightwards arrow 0 below fraction numerator left square bracket italic cos open parentheses x close parentheses open parentheses 1 minus x close parentheses plus italic sin open parentheses x close parentheses open parentheses 0 minus 1 close parentheses right square bracket over denominator 1 end fraction$ (Apply theL'Hospital's rule)

$italic lim with x rightwards arrow 0 below fraction numerator open parentheses italic sin open parentheses x close parentheses close parentheses open parentheses 1 minus x close parentheses over denominator x end fraction equal fraction numerator left square bracket italic cos open parentheses 0 close parentheses open parentheses 1 minus 0 close parentheses plus italic sin open parentheses 0 close parentheses open parentheses 0 minus 1 close parentheses right square bracket over denominator 1 end fraction$ (Substitute x = 0 )

$italic lim with x rightwards arrow 0 below fraction numerator open parentheses italic sin open parentheses x close parentheses close parentheses open parentheses 1 minus x close parentheses over denominator x end fraction equal fraction numerator left square bracket 1 open parentheses 1 close parentheses plus open parentheses 0 close parentheses open parentheses minus 1 close parentheses right square bracket over denominator 1 end fraction$

Most popular tags

L'Hopital question help!????????????????

Please log in or register to add a comment.

Please log in or register to answer this question.

2 Answers

Please log in or register to add a comment.

Please log in or register to add a comment.

Related questions