Let f:(0, ) R be a differentiable function defined as f(x)= _ n _ r=1 ^n 1 2^ 2 r ^2 x 2^r . Then which of the following must be correct?

Question

Quantrex Academy · Accepted Answer

Correct answer: C. _ x 0⁺ f(x)= 1 3

f(x)= 1 2^2 ^2 x 2 + 1 2^4 ^2 x 2^2 + 1 2^6 ^2 x 2^3 + Let g(x)= f(x) d x aligned & = 1 2 x 2 + 1 2^2 x 2^2 + 1 2^3 x 2^3 + . +C & = _ n 1 2^n x 2^n - x+C & = 1 x - x+C f(x)= cosec ^2 x- 1 x^2 aligned f^ (x)=-2 cosec ^2 x x+ 2 x^3

Let f:(0, ) R be a differentiable function defined as f(x)= _ n _ r=1 ^n 1 2^ 2 r ^2 x 2^r . Then which of the following must be correct?

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Correct answer

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