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InterviewSolution
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परिगणना कीजिए `:lim_(xto(pi)/(2))(sqrt2-sqrt(1+sinx))/(sqrt2*cos ^(2)x)` |
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Answer» प्रश्नानुसार, `lim_(xto(pi)/(2))(sqrt2-sqrt(1+sinx))/(sqrt2*cos^(2)x)=lim_(xto(pi)/(2))(sqrt2-sqrt(1+sinx))/(sqrt2*cos^(2)x)xx(sqrt2+sqrt(1+sinx))/(sqrt2+sqrt(1+sinx))` `=lim_(xto(pi)/(2)){(2-(1+sinx))/(sqrt2(1-sin^(2)x))xx(1)/(sqrt2+sqrt(1+sinx))}` `=lim_(xto(pi)/(2)){((1-sinx))/(sqrt2(1-sinx)(1+sinx))xx(1)/(sqrt2+sqrt(1+sinx))}` `=lim_(xto(pi)/(2))(1)/(sqrt2(1+sinx))xx(1)/(sqrt2+sqrt(1+sinx))` `=(1)/(2sqrt2)xx(1)/(sqrt2xxsqrt2)` `=1/8` |
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