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Application Of Derivatives

Question
CBSEENMA12035611
Wired Faculty App

If y = x4 + 10 and x changes from 2 to 1.99, find the approximate change in y.

Solution

Here  y = x4 + 10
  therefore space space dy over dx space equals space 4 straight x cubed because space space space straight x space changes space from space 2 space to space 1.99 therefore space space straight x space equals space 2 comma space space δx space equals space dx space equals space minus 0.01 Now space δy space is space approximately space equal space to space dy space and space space space space space space space space dy space equals space dy over dx dx space equals space 4 straight x cubed dx space space space space space space space space space space space space space equals space 4 left parenthesis 2 right parenthesis cubed space left parenthesis negative 0.01 right parenthesis space equals space minus 32 space cross times space 0.01 space equals space minus 0.32 when space straight x space equals space 2 comma space space space space space straight y space equals space left parenthesis 2 right parenthesis to the power of 4 plus 10 space equals space 16 plus 10 space equals space 26 therefore space space space space space straight y space plus space δy space equals space 26 space plus left parenthesis negative 0.32 right parenthesis space equals space 25.68 therefore space space space space space space space space space straight y space changes space from space 26 space to space 25.68.

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