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[" and "r" such that "],[" mainder.Thus,...

[" and "r" such that "],[" mainder.Thus,in "],[" 5,we prove that "]

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Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest integer function, prove that Rf=4^(2n+1)

Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest integer function, prove that Rf=4^(2n+1)

Through this experiment we prove

If f:[-5,\ 5]->R is differentiable and if f^(prime)(x) doesnt vanish anywhere, then prove that f(-5)!=f(5) .

If f[-5,5] to R , is a differentiable function and if f'(x) does not vanish anywhere, then prove that f(-5)!=f(5) .

If 12p_(r)=1320, then prove that r=3