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  • Let f(x) = x tan^-1 (x^2)+x^4 . Let f^k(x) denotes kth derivative of f(x) wrt x, k belong to N .if f^2m(0) is not equal to 0 , then m equals

Let f(x) = x tan^-1 (x^2)+x^4 . Let f^k(x) denotes kth derivative of f(x) wrt x, k belong to N .if f^2m(0) is not equal to 0 , then m equals

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  Solution:       Let    g(x)=x an^-1(x^2)  it is odd function 

       So ,            g^2m(0)=0.  Let      h(x)=x^4

      So ,            f(x)=g(x)+h(x)Rightarrow f^2m(0)

                                    =g^2m(0)+h^2m(0)\ \ Rightarrow hspace0.5cm=h^2m eq 0

    It happens when   2m=4Rightarrow m=2                                                                                  

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Deependra Verma

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