InterviewSolution
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InterviewSolution
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`sqrt(sin 3x)` को प्रथम सिद्धांत से अवलंकित कीजिएः |
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Answer» माना `y=sqrt(sin 3x)` `Rightarrow y+deltay=sqrt(sin 3(x+deltax))` `Rightarrow y+deltay-y=sqrt(sin 3(x+8x))-sqrt(sin 3x)` `Rightarrow (deltay)/(deltax)=(sqrt(sin 3(x+deltax))-sqrt(sin 3x))/(deltax)` अब `(dy)/(dx)=underset(deltax to 0)lim (deltay)/(deltax)` `=underset(deltax to 0)lim [({sqrt(sin (3x+3deltax))-sqrt(sin 3x)})/(deltax)xx({sqrt(sin 3x+3deltax)+sqrt(sin3x)})/({sqrt(sin(3x+3deltax))+sqrt(sin 3x)})]` `=underset(deltax to 0)lim ([sin (3x+3deltax)-sin3x])/(deltax.{sqrt(sin(3x+3deltax))+sqrt(sin 3x)})` `=underset(deltax to 0)lim (2 cos (3x+(3)/(2)deltax)sin((3)/(2)deltax))/(deltax.{sqrt(sin (3x+3deltax))+sqrt(sin 3x)})` `=underset(deltax to 0)lim [2cos(3x+(3)/(2)deltax).(sin((3)/(2)deltax))/(((3)/(2)deltax))xx(3)/(2) (1)/(sqrt(sin (3x+3deltax))+sqrt(sin 3x))]` `=underset(deltax to 0)lim cos (3x+(3)/(2)deltax).underset((3)/(2)deltax to 0)lim (sin((3)/(2)deltax))/(((3)/(2)deltax)).3 underset(deltax to 0)lim (1)/(sqrt(sin(3x+3deltax))+sqrt(sin 3x))` `=3 cos 3x xx 1 xx (1)/(2sqrt(sin3x))=(3 cos 3x)/(2 sqrtsin 3x)` |
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