My Math Forum Hard limit problem one variable calculus

 Calculus Calculus Math Forum

December 14th, 2016, 02:37 AM   #21
Newbie

Joined: Dec 2016
From: Sweden

Posts: 13
Thanks: 1

Quote:
 Originally Posted by agentredlum Try breaking up the math tex into several lines so you can more easily identify where the problem is , like this [M ATH] ...... [/M ATH] [M ATH] ..... [/M ATH] [M ATH] ..... [/M ATH]
I did.
Then I simplified it.

Huggs & Kisses

December 14th, 2016, 02:41 AM   #22
Newbie

Joined: Dec 2016
From: Sweden

Posts: 13
Thanks: 1

Quote:
 Originally Posted by agentredlum Now that I think more about it, there is an easier approach ... Would you agree that $\displaystyle h = \sqrt{|h|} \sqrt{|h|} \text{sgn}(h)$ ? If you do, then $\displaystyle \frac{\sqrt{|h|}}{h} = \frac{\sqrt{|h|}}{\sqrt{|h|} \sqrt{|h|} \text{sgn}(h)}$ Now just cancel common factor $\displaystyle \sqrt{|h|}$ from numerator and denominator to get the final result in my previous post. I originally set on a path and followed it, not the quickest.
And I started writing in another window on my phone.
Then used copy paste.
Didn't even see you already simplified it.

Last edited by skipjack; December 14th, 2016 at 10:40 AM.

December 14th, 2016, 02:44 AM   #23
Math Team

Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Quote:
 Originally Posted by Luciferis Which could have been realised more easily with. $\displaystyle \frac{\sqrt{|h|}}{h} = \frac{\sqrt{|h|}}{|h|\text{sgn}(h)} = \frac{\sqrt{|h|}}{\sqrt{|h|}\sqrt{|h|}\text{sgn}(h )} = \frac{1}{\sqrt{|h|}\text{sgn}(h)}$
I agree, nice presentation.

Note that the introduction of the sgn(h) notation makes it absolutely clear that the 2-sided limit does not exist since h --> 0 from both the positive and the negative.

Last edited by skipjack; December 14th, 2016 at 10:38 AM.

 Tags abs, calculus, hard, limit, newton, point, problem, quotient, variable

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mathkid Calculus 2 September 16th, 2012 02:31 PM claudillama Calculus 3 January 31st, 2012 07:52 PM netmaxweb Calculus 2 October 15th, 2011 01:11 PM Zeefinity Calculus 2 February 25th, 2011 06:17 AM Zeefinity Calculus 2 February 15th, 2011 08:01 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top