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February 21st, 2011, 07:01 PM  #1 
Senior Member Joined: Feb 2011 Posts: 118 Thanks: 0  Derivatives: Differential and Linear approximation HELP
Hi, I got a review sheet, and I'm having trouble solving these particular questions on differentials and linear approximations...I need some assistance please. 1) In a manufacturing process, ball bearings must be made with radius of 0.5 mm, with a maximum error in the radius of (+or)0.018 mm. Estimate the maximum error in the volume of the ball bearing. The formula for the volume of the sphere is_______. If an error (delta)r is made in measuring the radius of the sphere, the maximum error in the volume is (delta)V=______________. Rather than calculating (delta)V, approximate (delta)V with dV, wher dV=_________. Replacing r with _________ and dr=(delta)r with (+ or )_________ gives dV= (+ or )_________ The maximum error in the volume is about____________mm(cubed). 2)The demand function for a product is given by p=f(q)=90?sqrt(q). Where p is the price per unit in dollars for q units. Use the linear approximation to approximate the price when 2024 units are demanded. Solution: We want to approximate f(2024). From: f(q)*approximate symbol*=L(q)=f(a)+f'(a)(qa) and the fact that f'(a)___________(1/sqrt(a) or 1/2(sqrt(a)) or 1/2(sqrt(a)) or 1/sqrt(a) ) we choose a=_________. From f(2025)=_______ and f'(2025)=__________ we get f(2024)*approximate symbol*_________. hence, the price per unit when 2024 units are demanded is approximately $________. IF anything is unclear on my part, describing the problems, please let me know.. Thank you. 
February 22nd, 2011, 08:07 PM  #2 
Senior Member Joined: Feb 2011 Posts: 118 Thanks: 0  Re: Derivatives: Differential and Linear approximation HELP
I have figured out the second question that is given. So I'm only still stuck on the first question. Thanks!

February 22nd, 2011, 09:29 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Derivatives: Differential and Linear approximation HELP
The formula for the volume V of a sphere of radius r is: Thus, and Replacing r with 0.5 mm and dr = ?r with ±0.018 mm gives: Thus, the maximum error is about 0.0565 mm³. 
February 23rd, 2011, 04:41 PM  #4 
Senior Member Joined: Feb 2011 Posts: 118 Thanks: 0  Re: Derivatives: Differential and Linear approximation HELP
Thanks a lot!

February 24th, 2011, 06:08 PM  #5  
Newbie Joined: Feb 2011 Posts: 13 Thanks: 0  Re: Derivatives: Differential and Linear approximation HELP Quote:
 
February 24th, 2011, 06:28 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Derivatives: Differential and Linear approximation HELP
We may use the linear approximation to f(q) by the pointslope formula: With we have so and since and we choose a = 2025. Thus with: and we have: This is very close to the actual value of f(2024). 

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