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 January 9th, 2019, 10:22 AM #1 Member   Joined: Feb 2018 From: Iran Posts: 50 Thanks: 3 Linear approximation Using linear approximation calculate sqrt(99)? January 9th, 2019, 11:00 AM   #2
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Quote:
 Originally Posted by Elize Using linear approximation calculate sqrt(99)?
Let $\displaystyle y(x) = \sqrt{x}$. Expand this in a Taylor series (with x small compareed to a):
$\displaystyle y(a - x) \approx y(a) + \left . \dfrac{dy}{dx} \right | _{x = a}\cdot (a - x)$

So let a = 100 and x = 1.

-Dan January 9th, 2019, 12:55 PM   #3
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Quote:
 Originally Posted by Elize Using linear approximation calculate sqrt(99)?
I'm lazy: slightly less than 10  January 9th, 2019, 02:10 PM #4 Senior Member   Joined: Dec 2015 From: somewhere Posts: 536 Thanks: 81 It is between 9 and 10 and approximation will change for different values of x and a $\displaystyle y(x)\approx y(a)+y’(a)(x-a)$ January 9th, 2019, 04:50 PM   #5
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Quote:
 Originally Posted by topsquark Let $\displaystyle y(x) = \sqrt{x}$. Expand this in a Taylor series (with x small compareed to a): $\displaystyle y(a - x) \approx y(a) + \left . \dfrac{dy}{dx} \right | _{x = a}\cdot (a - x)$ So let a = 100 and x = 1. -Dan
Shouldn't that be
$\displaystyle y(a - x) \approx y(a) - \left . \dfrac{dy}{dx} \right | _{x = a}\cdot x$ January 9th, 2019, 04:58 PM   #6
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Quote:
 Originally Posted by v8archie Shouldn't that be $\displaystyle y(a - x) \approx y(a) - \left . \dfrac{dy}{dx} \right | _{x = a}\cdot x$ Thanks for the catch.

-Dan Tags approximation, linear Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post RGNIT Calculus 0 March 20th, 2014 11:21 PM pdeep Calculus 4 November 2nd, 2011 03:11 AM Luckyy Calculus 2 February 24th, 2011 05:43 PM Oranges'n'Lemons Calculus 1 February 20th, 2011 09:31 PM shango Calculus 1 October 27th, 2009 02:45 PM

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