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2- 3x- 3X- %3D

2- 3x- 3X- %3D

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.6: Rules For Multiplication
Problem 34WE
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DERIVATIVE USING DELTA METHOD.

y = 2- 3x-
Transcribed Image Text:y = 2- 3x-
1. Increment x by small amount Ax and y by Ay. y+ Ay = f( x+ Ax) 2. Substitute y = f(x) and solve for Ay. Ay = f( x+ Ax) - f(x) 3. Perform some suitable operation to the right hand member of the result of Step 2, so that Ax will be its factor. This should be done to satisfy the limit of the quotient, that is, the limit of the denominator is not zero. 4. Divide both side of the equation by Ax. Ay_ f( x + Ax) – [(x) Ax Ax 5. Determine the limit of both sides as Ax approaches zero. lim X0 Ax = lim f( x+ Ax) – f(x) Ax Ax-0 The steps above can be summarized as follows: y = f(x) y + Ay = f( x+ Ax) Step 1 Ay = f( x+ Ax) - f(x) Steps 2 and 3 Ay f( x+ Ax) – f(x) Step 4 Ax Ax dy f( x+ Ax) - f(x) lim Ay = lim Ax-0 Step 5 dx x-0 Ax Ar ala II
Transcribed Image Text:1. Increment x by small amount Ax and y by Ay. y+ Ay = f( x+ Ax) 2. Substitute y = f(x) and solve for Ay. Ay = f( x+ Ax) - f(x) 3. Perform some suitable operation to the right hand member of the result of Step 2, so that Ax will be its factor. This should be done to satisfy the limit of the quotient, that is, the limit of the denominator is not zero. 4. Divide both side of the equation by Ax. Ay_ f( x + Ax) – [(x) Ax Ax 5. Determine the limit of both sides as Ax approaches zero. lim X0 Ax = lim f( x+ Ax) – f(x) Ax Ax-0 The steps above can be summarized as follows: y = f(x) y + Ay = f( x+ Ax) Step 1 Ay = f( x+ Ax) - f(x) Steps 2 and 3 Ay f( x+ Ax) – f(x) Step 4 Ax Ax dy f( x+ Ax) - f(x) lim Ay = lim Ax-0 Step 5 dx x-0 Ax Ar ala II
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