InterviewSolution
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InterviewSolution
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If`y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se q u a lto``(a y)/(xsqrt(a^2-x^2))`(b) `(a y)/(sqrt(a^2-x^2))``(a y)/(xsqrt(a^2-x^2))`(d) none of theseA. `(ay)/(xsqrt(a^(2)-x^(2)))`B. `(ay)/(sqrt(a^(2)-x^(2)))`C. `(ay)/(xsqrt(x^(2)-a^(2)))`D. none of these |
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Answer» `y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x))` `=((sqrt(a+x)-sqrt(a-x))^(2))/((a+x)-(a-x))` `=((a+x)+(a-x)-2(sqrt(a^(2)-x^(2))))/(2x)` `=(2a-2sqrt(a^(2)-x^(2)))/(2x)=(a-sqrt(a^(2)-x^(2)))/(x)" (1)"` Differentiating w.r.t. x, we get `(dy)/(dx)=(x[-(1)/(2sqrt(a^(2)-x^(2)))(-2x)]-(a-sqrt(a^(2)-x^(2))))/(x^(2))` `=(x^(2)-asqrt(a^(2)-x^(2)+a^(2)-x^(2)))/(x^(2)sqrt(a^(2)-x^(2)))=(a(a-sqrt(a^(2)-x^(2))))/(x^(2)sqrt(a^(2)-x^(2)))` `(a)/(xsqrt(a^(2)-x^(2)))[(a-sqrt(a^(2)-x^(2)))/(x)]=(ay)/(xsqrt(a^(2)-x^(2)))" [by (1)]"` |
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