September 14th, 2013, 03:50 AM  #1 
Member Joined: Sep 2012 Posts: 61 Thanks: 0  Limit with cube and square root
How to solve this: lim [cuberoot(7+x^3)squareroot(3+x^2)]/(x1) x>1 I don't know what to do when I have cube and square root at the same time. 
September 14th, 2013, 04:41 AM  #2 
Member Joined: Apr 2013 Posts: 52 Thanks: 0  Re: Limit with cube and square root
Since both the numerator and the denominator equal to zero,when x>1,you can apply the "L'Hospital's Rule",that allows you to evaluate the limit more easily!! :P Are you familiar with this rule,or should I explain it further to you?? 
September 14th, 2013, 05:24 AM  #3 
Member Joined: Sep 2012 Posts: 61 Thanks: 0  Re: Limit with cube and square root
I need to do this without differentiation.

September 15th, 2013, 12:09 AM  #4 
Member Joined: Sep 2012 Posts: 61 Thanks: 0  Re: Limit with cube and square root
Any idea, please?

September 16th, 2013, 08:21 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Limit with cube and square root
Assuming the limit exists, 
September 16th, 2013, 10:52 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Limit with cube and square root
I think the limit must exist. Here's why: Reversing the sign of L gives the same result. Hence the limit exists and is equal to 
September 16th, 2013, 11:26 AM  #7 
Member Joined: Sep 2012 Posts: 61 Thanks: 0  Re: Limit with cube and square root
I didn't understand the part I attached. Could you explain more deeply what you did, and with what purpose?

September 16th, 2013, 11:42 AM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Limit with cube and square root Ok? 
September 17th, 2013, 07:22 AM  #9 
Member Joined: Sep 2012 Posts: 61 Thanks: 0  Re: Limit with cube and square root
It's okay, thanks.


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cube, limit, root, square 
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