Consider the implicit function ( w ( x ) + 1 ) e w ( x ) = x .I need to approximate w ( 1.1 ) using the fact that w ( 1 ) = 0.Could you give me any hints?

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Consider the implicit function  (  w  (  x  )  +  1  )      e          w      (      x      )        =  x  .I need to approximate   w  (  1.1  ) using the fact that   w  (  1  )  =  0.Could you give me any hints?

seguidora1e · Accepted Answer

Consider the implicit equation  F  =  (  y  +  1  )      e    y    −  x  =  0and compute the partial derivatives      F    x    ′    =  −  1      F    y    ′    =  (  y  +  2  )      e    y  Now, from implicit differentiation            d      y              d      x        =  −            F      x      ′              F      y      ′        =      1          (      y      +      2      )              e        y            So  y  (  1.1  )  ≈  y  (  1  )  +            1.1      −      1.0              (      y      (      1      )      +      2      )              e                  y          (          1          )                      =  0  +      0.1          (      0      +      2      )              e                  0                      =  0.05You could also compute             d      x              d      y       and deduce             d      y              d      x       from it. This is probably the simplest.

Consider the implicit function (w(x)+1)e^(w(x))=x. I need to approximate w(1.1) using the fact that w(1)=0.

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