Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,459 questions

17,854 answers

1,446 comments

789,628 users

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

0 votes
I need to use L'Hopital's rule to find this limit: the limit as x approaches zero from the right, (sin x) times square root of [(1-x)/x]
asked Apr 19, 2013 in CALCULUS by mathgirl Apprentice

2 Answers

0 votes

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

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 1                                                              (Simplify)

 

answered Apr 19, 2013 by diane Scholar
0 votes

image

image

image

Apply L ' Hopital rule.

image

image

image

image

image

image

image

image

answered Jul 28, 2014 by david Expert

Related questions

asked Oct 25, 2014 in TRIGONOMETRY by anonymous
asked Aug 5, 2014 in PRECALCULUS by anonymous
asked Feb 7, 2015 in CALCULUS by anonymous
asked Dec 8, 2014 in CALCULUS by anonymous
asked Aug 11, 2015 in CALCULUS by anonymous
asked Aug 11, 2015 in CALCULUS by anonymous
asked Aug 11, 2015 in CALCULUS by anonymous
asked Jul 10, 2015 in CALCULUS by anonymous
asked Jun 2, 2015 in CALCULUS by anonymous
asked Jun 2, 2015 in CALCULUS by anonymous
asked Jun 2, 2015 in CALCULUS by anonymous
asked Jun 2, 2015 in CALCULUS by anonymous
asked Jun 1, 2015 in CALCULUS by anonymous
asked Apr 27, 2015 in CALCULUS by anonymous
asked Apr 27, 2015 in CALCULUS by anonymous
...