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Hey tell me the mistake... I have proved 2=1 x 2 = x*x =x+x+x+x+...(x times) lets take derivatives both side... d/dx(x 2 )=d/dx(x+x+x+x+...(xtimes)) 2x=1+1+1+1+...(x times) 2x=x 2=1 I can’t find the mistake...this is not possible..

 
Hey tell me the mistake... I have proved 2=1
 
x2= x*x
    =x+x+x+x+...(x times)
lets take derivatives both side...
d/dx(x2)=d/dx(x+x+x+x+...(xtimes))
2x=1+1+1+1+...(x times)
2x=x
2=1
 I can’t find the mistake...this is not possible..

Grade:11

1 Answers

Arun
25750 Points
5 years ago
It is pretty clear that, adding a number `x` times makes sense only if `x` is a positive integer. Hence the function X^2 is written this way. So the function X^2 exizts only for integers. This is against the basic requirement of differentiation. A function is differentiable only if it is continuous. But our function is defined only for integers. So it is not continuous. Its discrete and hence not differentiable. Hence wrong.

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