Question

prove that x , x+1, x(x+1) = x(x+1)+1​

Answer 1

Answer:

1

Down vote

Prove that xx+1<ln(1+x)<x for x>−1,x≠0

real-analysis derivatives inequality proof-writing logarithms

I found this problem in the mean value theorem section in a real analysis book.

I did not know, how to use the mean value theorem but I tried to find f′ and I found

1(x+1)2<11+x<1.

Clearly, 1(x+1)2decrease faster than11+x, when x grow larger.

Answer 2

Answer:

if x is not equal to zero then prove it by equation method