Effect of Significant Digits on Derivative of a Function Autar Kaw, Ana Catalina TorresUniversity of South FloridaUnited States of Americakaw@eng.usf.eduIntroductionThis worksheet demonstrates the use of Maple to illustrate the effect of significant digits on the numerical calculation of the Forward Difference Approximation of the first derivative of continuous functions. Forward Difference Approximation of the first derivative uses a point h ahead of the given value of x at which the derivate of f(x) is to be found.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIidGJ0YvRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYlUSJ4RidGL0YyRi9GMkYvRjItRjY2LlEpJmFwcHJveDtGJ0YvRjJGOUY8Rj5GQEZCRkRGRi9GSVEsMC4yNzc3Nzc4ZW1GJy9GTEZaLUkmbWZyYWNHRiQ2KC1GIzYpRistRk82JS1GIzYnRlMtRjY2LlEiK0YnRi9GMkY5RjxGPkZARkJGREZGL0ZJUSwwLjIyMjIyMjJlbUYnL0ZMRmNvLUYsNiVRImhGJ0YvRjJGL0YyRi9GMi1GNjYuUSgmbWludXM7RidGL0YyRjlGPEY+RkBGQkZERkZGYm9GZG9GKy1GTzYkRlEvRjNRJ25vcm1hbEYnRi9GMi1GIzYlRmVvRi9GMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZnAvJSliZXZlbGxlZEdGO0YvRjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbW9HRiQ2P1EhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHRjcvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGNy8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjcvJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGZm9GL0YyRjVGOEY6RjxGPkZARkNGRkZIRkpGTEZORlBGUkZURlk=InitializationLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JlEocmVzdGFydEYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiO0YnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGVy8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GOTYuUSJ+RidGL0Y8Rj4vRkFGMUZCRkRGRkZIRkpGTC9GUEZOLUYsNiZRJXdpdGhGJ0YvRjJGNUZqbi1JKG1mZW5jZWRHRiQ2JS1GIzYoLUYsNiZRJnBsb3RzRidGL0YyRjUvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJ0YvLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2V4ZWN1dGFibGVHRjFGPC9GNlElYm9sZEYnLyUrZm9udHdlaWdodEdGY3AtRjk2LlEiOkYnRi9GPEY+Rl1vRkJGREZGRkhGSi9GTUZRRk9Gam9GL0ZdcEZgcEY8Section 1: InputThe following simulation approximates the first derivative of a function using Forward Difference Approximation with fixed number of significant digits used in the calculation. The user inputs are a) function, f(x) b) point at which the derivative is to be found, xv c) step size, h d) The lowest and highest number of significant digits user wants to use in the calcluation. The user should choose the lowest number to be at least 2.The outputs include a) exact value c) true error and absolute relative true error as a function of the number of significant digits.FunctionLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUZHNiVRInhGJ0ZKRk1GL0YvRi8=. 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 of x at which f(x) is desired, 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 size, 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Lowest number of Significant Digits and Highest Number of Significant 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 is the end of the user section. All the information must be entered before proceeding to the next section. Re-execute the program.Section 2: ProcedureThe following procedure estimates the solution of first derivate of an equation at a point xv.f (x) = function xv = value at which the solution is desired h = step size valuedig = number of significant digits used in the calculationLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZHLUkjbWlHRiQ2JlEkRkRERicvJSVib2xkR1EmZmFsc2VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSomY29sb25lcTtGJ0YvL0Y2USdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk4tRjk2LlElcHJvY0YnL0Y2USVib2xkRicvJStmb250d2VpZ2h0R0ZVRj5GQEZCRkRGRkZIRkovRk1RJjAuMGVtRicvRlBGWS1JKG1mZW5jZWRHRiQ2JS1GIzYuLUYsNiZRImZGJ0YvRjJGNS1GOTYuUSIsRidGL0Y8Rj4vRkFGNEZCRkRGRkZIRkpGWC9GUFEsMC4zMzMzMzMzZW1GJy1GLDYmUSN4dkYnRi9GMkY1Rl1vLUYsNiZRImhGJ0YvRjJGNUZdby1GLDYmUSRkaWdGJ0YvRjJGNS8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnRi8vJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdGMUY8Ri9GPC1GOTY/USFGJ0ZccC8lJXNpemVHUSMxMkYnRi8vRjNGMS8lKnVuZGVybGluZUdGMS8lKnN1YnNjcmlwdEdGMS8lLHN1cGVyc2NyaXB0R0YxRl9wLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGMUZicC8lKXJlYWRvbmx5R0YxLyUpY29tcG9zZWRHRjEvJSpjb252ZXJ0ZWRHRjEvJStpbXNlbGVjdGVkR0YxLyUscGxhY2Vob2xkZXJHRjEvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjEvJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RidGPEY+RkBGQkZERkZGSEZKRlhGWi1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0Zqci8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GOTYuUSJ+RidGL0Y8Rj5GQEZCRkRGRkZIRkpGWEZaLUY5Ni5RJmxvY2FsRidGVEZWRj5GQEZCRkRGRkZIRkpGWEZaRmNzLUYsNiZRJmRlcml2RidGL0YyRjUtRjk2LlEiOkYnRi9GPEY+RkBGQkZERkZGSEZKRkxGT0ZlckZjcy1GLDYmUSdEaWdpdHNGJ0YvRjJGNUY4RmlvRlx0RmVyRmlzRjgtSSZtZnJhY0dGJDYoLUZmbjYlLUYjNixGam4tRmZuNiUtRiM2KkZjby1GOTYuUSIrRidGL0Y8Rj5GQEZCRkRGRkZIRkovRk1RLDAuMjIyMjIyMmVtRicvRlBGYXVGZm9GXHBGL0ZfcEZicEY8Ri9GPC1GOTYuUSgmbWludXM7RidGL0Y8Rj5GQEZCRkRGRkZIRkpGYHVGYnVGam4tRmZuNiUtRiM2KEZjb0ZccEYvRl9wRmJwRjxGL0Y8RlxwRi9GX3BGYnBGPEYvRjwtRiM2KEZmb0ZccEYvRl9wRmJwRjwvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmF2LyUpYmV2ZWxsZWRHRjEtRjk2LlEiO0YnRi9GPEY+RmBvRkJGREZGRkhGSkZYRk9GZXItRjk2LlEncmV0dXJuRidGVEZWRj5GQEZCRkRGRkZIRkpGWEZaRmNzLUZmbjYlLUYjNihGaXNGXHBGL0ZfcEZicEY8Ri9GPEZcdEZlci1GOTYuUSRlbmRGJ0ZURlZGPkZARkJGREZGRkhGSkZYRlpGY3NGUUZcdEZccEYvRl9wRmJwRjw=Section 3: CalculationThe exact value Ev of the first derivative of the equation:First, using the diff command the solution is found. In a second step, the exact value of the derivative is shown. 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 next loop calculates the following:Av: Approximate value of the first derivative using Forward Difference Approximation by calling the procedure "FDD"Et: True erroret: Absolute relative true percentage errorEa: Approximate errorea: Absolute relative approximate percentage 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The loop calculates the approximate value of the first derivative, the corresponding true error and relative true error as a function of the number of significant digits used in the calculations.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Section 4: SpreadsheetThe next table shows the approximate value, true error, and the absolute relative true percentage error as a function of the number of significant digits used in the calculations.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 5: GraphsThe following graphs show the approximate solution, true error and absolute relative true error as a function of the number of significant digits used.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 Differentiation of Continuous Functions. http://numericalmethods.eng.usf.edu/mws/gen/02difQuestionsThe velocity of a rocket is given 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Use Forward Divided Difference method with a step size of 0.25 to find the acceleration at t=5s using different number of significant digits.ConclusionsThe effect of significant digits on the calculation of the first derivative using Forward Difference approximation is studied.Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. 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