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CBSE Class 12-science Answered

Find the approximate value of f(4.02) where the function is given by f(x)=x- 3x+ x + 2   
Asked by Topperlearning User | 05 Aug, 2014, 12:53: PM
Expert Answer

 

Here space take space straight x equals 4 space and space increment straight x space equals space 0.02
As space you space know space that space
increment straight y equals straight f left parenthesis straight x plus increment straight x right parenthesis minus straight f left parenthesis straight x right parenthesis
Which space means space straight f left parenthesis straight x right parenthesis space is
straight f apostrophe left parenthesis straight x right parenthesis equals 3 straight x squared minus 6 straight x plus 1 comma space which space is space approximately space equal space to space fraction numerator increment straight y over denominator increment straight x end fraction
Therefore space straight f left parenthesis straight x plus increment straight x right parenthesis equals straight f left parenthesis straight x right parenthesis plus straight f apostrophe left parenthesis straight x right parenthesis. increment straight x
Using space the space values space of space straight f left parenthesis straight x right parenthesis space and space straight f apostrophe left parenthesis straight x right parenthesis space in space the space above space equation
rightwards double arrow straight f left parenthesis 4.02 right parenthesis almost equal to open square brackets 4 cubed minus 3 left parenthesis 4 right parenthesis squared plus 4 plus 2 close square brackets plus open square brackets 3 left parenthesis 4 right parenthesis squared minus 6 left parenthesis 4 right parenthesis plus 1 close square brackets cross times 0.02
equals 22 plus 25 cross times 0.02
equals 22 plus 0.5 equals 22.5
Hence space the space approximate space value space of space straight f left parenthesis 4.02 right parenthesis space is space 22.5

Answered by | 05 Aug, 2014, 02:53: PM
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