October 29th, 2012, 12:28 PM  #1 
Newbie Joined: Dec 2011 Posts: 13 Thanks: 0  Calculus, limits, four problems
Hello to everyone! I have four problem I can't solve. Please, help me. Thanks a lot beforehand 
October 29th, 2012, 12:34 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Calculus, limits, four problems
First, are you "allowed" to use L'Hôpital's rule?

October 29th, 2012, 12:57 PM  #3 
Newbie Joined: Dec 2011 Posts: 13 Thanks: 0  Re: Calculus, limits, four problems
I don't know about L'Hôpital's rule yet. I just have started to learn calculus. For examples of solutions I try to insight in understanding of limits. So, I ask of you to solve this limits and try to explain me how you do it.

October 29th, 2012, 01:07 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Calculus, limits, four problems
Okay, I just wanted to know first before working solutions, only to be told afterwards that L'Hôpital's rule is not allowed. It happens quite a bit with these types of limits. 
October 29th, 2012, 11:50 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Calculus, limits, four problems
I'll work the first one: 1.) I would break this up into two limits: Here, the degree in the denominator is greater than that of the numerator, hence: The degree in the numerator and denominator is the same, so we take the ratio of the leading coefficients: And so we have: 
October 30th, 2012, 03:47 AM  #6 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Calculus, limits, four problems
If you mean by tg(x) tan(x) then the third and fourth one can be solved by multiplying and dividing by the conjugate.

October 30th, 2012, 07:42 AM  #7  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Calculus, limits, four problems Hello, The Crisp! I'll do the last one . . . Quote: Multiply numerator and denominator by the conjugate: [color=beige]. . [/color] Divide numerator and denominator by [color=beige]. . [/color] Therefore:[color=beige] .[/color]  
October 30th, 2012, 09:08 AM  #8 
Newbie Joined: Dec 2011 Posts: 13 Thanks: 0  Re: Calculus, limits, four problems 
October 30th, 2012, 09:10 AM  #9 
Newbie Joined: Dec 2011 Posts: 13 Thanks: 0  Re: Calculus, limits, four problems
P.S. Sorry, Iforgot to rotate the picture 
October 31st, 2012, 11:16 AM  #10  
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Calculus, limits, four problems Quote:
 

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