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Question

Find the approximate value of (1.999)5
 


Solution

Let  x = 2 
and x=0.001
 Let y=x5
 On differentiating both sides w.r.t. x, we get
dydx=5x4Now,y=dydx.x=5x4×x=5×24×[0.001](1.999)5=y+y=25+(0.080)=320.080=31.920
 

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