My Math Forum ...and still. trouble with complex frac. in limit problem

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January 28th, 2010, 07:04 PM   #1
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...and still. trouble with complex frac. in limit problem

This is slightly embarrassing but I'll put my pride out of the way in hopes of learning what boneheaded thing I'm doing wrong so that I might correct it. Have to use the limit equation to find the derivative. super tedious. *sigh* I'm posting here rather than in calculus because the area in question (I think) is algebraic in nature.
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 January 28th, 2010, 07:06 PM #2 Member   Joined: Jan 2010 Posts: 82 Thanks: 0 Re: ...and still. trouble with complex frac. in limit problem well, i see the first thing wrong is that I multiplied by a -sqrt(g+h+1). doh!
 January 28th, 2010, 10:49 PM #3 Newbie   Joined: Jan 2010 Posts: 21 Thanks: 0 Re: ...and still. trouble with complex frac. in limit problem This is how I have made it : $f(x)=\frac{1}{\sqrt{x+1}}$ $f'(x_0)=\lim_{h\rightarrow 0} \frac{f(x_0+h)-f(x_0)}{h} = \lim_{h\rightarrow 0} \frac{ \frac{1}{\sqrt{x_0+h+1}} -\frac{1}{\sqrt{x_0+1}}}{h} = \lim_{h\rightarrow 0} \frac{\sqrt{x_0+1}-\sqrt{x_0+h+1}}{h\sqrt{(x_0+h+1)(x_0+1)}$ Eventually : $\lim_{h\rightarrow 0} \frac{x_0+1-h-x_0-1}{h\sqrt{(x_0+h+1)(x_0+1)}(\sqrt{x_0+1}+\sqrt{x_0 +h+1})}=$ $=-\lim_{h\rightarrow 0} \frac{h}{h\sqrt{(x_0+h+1)(x_0+1)}(\sqrt{x_0+1}+\sq rt{x_0+h+1})}=$ $=-\lim_{h\rightarrow 0} \frac{1}{\sqrt{(x_0+h+1)(x_0+1)}(\sqrt{x_0+1}+\sqr t{x_0+h+1})}=$ $=-\frac{1}{2|(x_0+1)|\sqrt{x_0+1}}$
 January 29th, 2010, 12:20 AM #4 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: ...and still. trouble with complex frac. in limit problem Not easy at all. A couple of typos: at the end of the longest line there is a factor (x0+1), where the 0 should be a subscript; and the denominator in the second-last line should not begin "h" (as it's been cancelled).
 January 29th, 2010, 12:56 AM #5 Newbie   Joined: Jan 2010 Posts: 21 Thanks: 0 Re: ...and still. trouble with complex frac. in limit problem Man! You got some good eyes, I haven't noticed it. 10x BTW - oddlogic, can I suggest that you try LaTeX or at least Windows Equation? I have tried OpenOffice Math but it wasn't pleasant. From experience, LaTeX is the best.
 January 29th, 2010, 04:06 AM #6 Member   Joined: Jan 2010 Posts: 82 Thanks: 0 Re: ...and still. trouble with complex frac. in limit problem yes you may fur. I was just trying to make it easier to read at my own expense and the expense in openoffice math is that it's finicky regarding parenthesis, thus time consuming. Thanks to you both. I will apply this immediately.
 January 29th, 2010, 08:55 AM #7 Member   Joined: Jan 2010 Posts: 82 Thanks: 0 Re: ...and still. trouble with complex frac. in limit problem omg- felt really silly after seeing these worked this morning. I was trying to make things much more complicated than they need be. These are simple problems. To anyone working these problems, there is no need to multiply anything on bottom (most of the time) and take your first opportunity to make the h=0. With that said, pay particular attention to the way that things cancel on top in early examples, so that you can apply it in later examples without much hassle.

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