A) y
B) \[y+\frac{{{x}^{n}}}{n!}\]
C) \[y-\frac{{{x}^{n}}}{n!}\]
D) \[y-1-\frac{{{x}^{n}}}{n!}\]
Correct Answer: C
Solution :
\[y=1+x+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{3}}}{3\,!}+....+\frac{{{x}^{n}}}{n\,!}\] Þ \[\left[ (\log \tan x+1)+\frac{1}{\tan x\log \tan x} \right]\] Þ \[\frac{dy}{dx}+\frac{{{x}^{n}}}{n\,!}=1+x+\frac{{{x}^{2}}}{2\,!}+.....+\frac{{{x}^{n}}}{n\,!}\]Þ \[\frac{dy}{dx}=y-\frac{{{x}^{n}}}{n\,!}\].You need to login to perform this action.
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