Percent Error Formula Calculus
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Using Differentials To Estimate Error
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Use Differentials To Estimate The Maximum Error In The Calculated Surface Area
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available. Most of the classes have practice problems with solutions available on the practice
Relative Error Differentials
problems pages. Also most classes have assignment problems for instructors to maximum error formula assign for homework (answers/solutions to the assignment problems are not given or available on the
Percent Error Differentials
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Linear Approximations... If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link http://www.freemathhelp.com/forum/threads/82005-Computing-Percent-Error-in-Linear-Approximations above to proceed. To start viewing messages, select the forum that you want http://www.phengkimving.com/calc_of_one_real_var/08_app_of_the_der_part_2/08_04_approx_of_err_in_measrmnt.htm to visit from the selection below. Results 1 to 4 of 4 Thread: Computing Percent Error in Linear Approximations... Thread Tools Show Printable Version Email this Page… Subscribe to this Thread… Search Thread Advanced Search Display Linear Mode Switch to Hybrid Mode Switch to Threaded Mode 07-02-2013,02:35 PM #1 StintedVisions View Profile View Forum differentials to Posts Private Message New Member Join Date Jul 2013 Posts 11 Computing Percent Error in Linear Approximations... We went over this section last week and the professor only covered half of it. I've got most of the answers except how to calculate the percent error. The question is: Use the following function to complete sections a-d. f(x)= x / x+2 ; a=1; f(1.1) I've gotten so far as to differentials to estimate a) f(x)~L(x)=(1/3)+(2/9)(x-1) b) was graphing, I got the graph correct c) f(1.1)~.356 everything above was correct, however part d) is computing the percent error. The formula is given 100*|(approx-exact)/exact|, I tried to compute it anyway and what I got and what the correct answer was were very different. Can anyone point me in the proper direction? Reply With Quote 07-02-2013,03:00 PM #2 Subhotosh Khan View Profile View Forum Posts Private Message Elite Member Join Date Jun 2007 Posts 15,798 Originally Posted by StintedVisions We went over this section last week and the professor only covered half of it. I've got most of the answers except how to calculate the percent error. The question is: Use the following function to complete sections a-d. f(x)= x / x+2 ; a=1; f(1.1) I've gotten so far as to a) f(x)~L(x)=(1/3)+(2/9)(x-1) b) was graphing, I got the graph correct c) f(1.1)~.356 everything above was correct, however part d) is computing the percent error. The formula is given 100*|(approx-exact)/exact|, I tried to compute it anyway and what I got and what the correct answer was were very different. Can anyone point me in the proper direction? Given equation is correct. Please show your work and answer - and we w
Solutions 1. Approximations If a quantity x (eg, side of a square) is obtained by measurement and a quantity y (eg, area of the square) is calculated as a function of x, say y = f(x), then any error involved in the measurement of x produces an error in the calculated value of y as well. Recall from Section 4.3 Part 2 that the Section 8.3 Part 1, we have: That is, the error in x is dx and the corresponding approximate error in y is dy = f '(x) dx. Fig. 1.1 Fig. 1.2 – 1st and 2nd axes: if 1,000 = xa – 1 then xa = 1,001, – 1st and 3rd axes: if 1,000 = xa + 1 then xa = 999, therefore xa is somewhere in [999, 1,001]. Example 1.1 Solution Let s be the side and A the area of the square. Then A = s2. The error of the side is ds = 1 m. The approximate error of the calculated area is: dA = 2s ds = 2(1,000)(1) = 2,000 m2. EOS Note that we calculate dA from the equation A = s2, since the values of s and ds are given. To find the differential of A we must have an equation relating A to s. So even if the measured value of the side is given we still define the variable s that takes on as a value the measured value. In general, when the measured value say V of a quantity and the error say E in the measurement are given, we define a variable say x for the quantity, so that x = V and dx = E, which will be used later on in the solution. When using the quantity, first use the variable x, not the value V, then use the value V when a value is to be obtained. Go To Problems & Solutions Return To Top Of Page 2. Types Of Errors A measurement of distance d1 yields d1 = 100 m with an error of 1 m. A measurement of distance d2 yields d2 = 1,000 m with an error of 1 m. Both measurements have the same absolute error of 1 m. However, intuitively we feel that measurement of d2 has a smaller error because it's 10 times larger and yet has the same absolute error. Clearly the effect of 1 m out of 1,000 m is smaller than that of 1 m out of 100 m. This leads us to consider an error relative to the size of the quantity being expressed. This relative error is accomplished by representing the absolute error as a fraction of the quantity being expressed. For example, the relative error for d1 is 1 m / 100 m = 1/100 = 0.01 and that for d2 is 1 m / 1,000 m = 1/1,000 = 0.001. As desired the relative error for d2 is smaller than that for d1. The percentage error is the absolute error as a percentage of the quantity being expressed. For example, the percentage error for d1 is (1 m / 100 m)(100/100) = (1/100)(100)% = (0.01)(100)% = 1% and that for d2 is (1 m / 1,000 m)(100/100) = (1/1,000)(100)% = (0.001)(100)% = 0.1%. We