My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
October 3rd, 2017, 10:51 AM   #1
Joined: Oct 2017
From: Delaware, Ohio

Posts: 2
Thanks: 0

Math Focus: Calculus
Derivative causing div-by-zero problem

I can figure out the 1st derivative of this by using the quotient rule, but if I try to use the definition of the derivative to figure it out, I can't escape running into a division-by-zero. Can anyone show me what algebra trick(s) I'm missing?
The function is f(x) =$\displaystyle \frac{2}{\sqrt{3-x}}$, so...

f'(x) = $\displaystyle \lim_{h\rightarrow 0}1/h \left [ \frac{2}{\sqrt{3-(x+h)}} - \frac{2}{\sqrt{3-x}}\right ]$

No matter how I manipulate this expression (many sheets of paper), I always wind up with 'h' as a factor in some denominator.
Can someone show me a way to solve this?
Uncle Ed
Uncle Ed is offline  
October 3rd, 2017, 06:20 PM   #2
Global Moderator
Joined: Dec 2006

Posts: 20,636
Thanks: 2080

After combining the fractions, multiplying the numerator and denominator by $\sqrt{3-x} + \sqrt{3-(x+h)}$ causes the numerator to become $2h$, allowing $h$ to be cancelled.
skipjack is offline  
October 4th, 2017, 05:55 AM   #3
Joined: Oct 2017
From: Delaware, Ohio

Posts: 2
Thanks: 0

Math Focus: Calculus
Thank you!

I thought I had tried using the conjugate but must have made an algebra mistake. This time it worked!
Uncle Ed is offline  
October 4th, 2017, 03:53 PM   #4
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Amazing, isn't it?

I once made the mistake of agreeing to teach a course in "Calculus for Business Administration". The text was assigned by the Department of Business Administration.

On one page the "laws of limits", "the limit of a sum is the sum of the limits", "the limit of a product is the product of the limits", and "the limit of a quotient is the quotient of the limits", with out proof, on one day. Given the course, I didn't mind that no proofs were given but on the very next page, it defined the derivative as the limit of the difference quotient, completely ignoring the fact that, since the difference quotient necessarily has denominator going to 0, none of those limit laws apply!
Country Boy is offline  

  My Math Forum > College Math Forum > Calculus

causing, derivative, divbyzero, problem

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Second Derivative Problem gorogoro56 Math 1 April 8th, 2015 05:28 AM
Derivative problem MathHatesMe Calculus 2 January 17th, 2015 12:50 PM
problem with simplification when taking the derivative of a derivative lackofimagination Calculus 1 July 6th, 2014 08:05 PM
Derivative problem azelio Algebra 2 October 17th, 2010 05:24 PM
Problem with derivative StevenMx Calculus 2 December 17th, 2008 10:55 AM

Copyright © 2019 My Math Forum. All rights reserved.