InterviewSolution
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InterviewSolution
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If `y=1=x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !),`show that `(dy)/(dx)-y+(x^n)/(n !)=0.` |
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Answer» `(dy)/(dx)=0+(1)/(1!)+(1)/(2!)(2x)+(1)/(3!)(3x^(2))+...+(1)/(n!)(nx^(n-1))` `=1+(x)/(1!)+(x^(2))/(2!)+...+(x^(n-1))/((n-1)!)` `={1+(x)/(1!)+(x^(2))/(2!)+...+(x^(n-1))/((n-1)!)+(x^n)/(n!)}-(x^(n))/(n!)` `=y-(x^(n))/(n!)` `"or "(dy)/(dx)-y+(x^(n))/(n!)=0` |
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