InterviewSolution
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InterviewSolution
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Find the coefficient of x in the expansion of `[sqrt(1+x^2) - x]^-1` in ascending power of x when `|x| |
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Answer» Correct Answer - D `[sqrt(1+x^(2))-x]^(-1)=(1)/(sqrt(1+x^(2))-x) xx ((sqrt(1+x^(2))+x))/((sqrt(1+x^(2))+x))` `= (sqrt(1+x^(2))+x)/(1+x^(2)-x^(2))=x+sqrt(1+x^(2))=x+(1+x^(2))^(1//2)` `= x+1+1/2 x^(2) + 1/2(-1/2) (x^(4))/(2!) + "….."` Therefore, the coefficient of `x^(4)` is `-1//8`. |
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