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Thursday, 23 January 2014

Approximate Value

 


Approximate Value :-

Let    y=f(x)

Now ,   Lt delta  x--->0 (delta  y)/(delta  x)=dy/dx ,

therefore from the definition of the limit

as    delta  x   approaches   0  ,

(delta  y)/(delta  x)  approaches  dy/dx

therefore ,  (delta  y)/(delta  x)=dy/dx

[approx . when   delta  x   is small]

or,  (delta  y)=dy/dx  (delta  x)

Thus ,  (delta  y)=dy/dx  (delta  x)

              [approximately]

Important Result  Essential For Problems :-

If   x   and   y   are functions of time ,  t  then

(dx/dt)=change of  x  in unit time 

         =rate of change of    x    .

and   (dy/dt)=change in   y  in unit time 

                  =rate of change of    y  .

Also , (dy/dx)=(dy/dt)/(dx/dt)