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If x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(...

If `x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(cos^(-1)t)` show that `(dy)/(dx)=-(y)/(x)`.

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If x=sqrt(a^(sin^(-1)t)), y= sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)= -(y)/(x) .

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If y = sqrt(x/(a))-sqrt(a/(x)) show that 2xy (dy)/(dx)=(x)/(a)-(a)/(x)

If x=(sin^(3)t)/(sqrt(cos 2t)) and y=(cos^(3)t)/( sqrt(cos 2t)) , show that (dy)/(dx)=0 at t=(pi)/(6) .

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CHHAYA PUBLICATION-QUESTION PAPER 2017-UNIT -3
  1. The value of int(-a)^(a)(xe^(x^4))/(1+x^2)dx is

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  2. The degree of the differential equation (d^3y)/(dx^3)+y=root3(1+(dy)/(...

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  3. If x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(cos^(-1)t) show that (dy)/(dx)...

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  4. Varify Rolle's theorem for the function f(x)=x^2-4x+3 in 1lexle3.

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  5. Evalute: int (cosx-cos2x)/(1-cosx)dx.

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  6. A particle starts with the velocity u and moves in a straight line, it...

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  7. Find the interval where f(x)=(1)/(1+x^2) decreases.

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  8. If f(x)=f(a+x), then prove that the value of int(a)^(a+t) f(x)dx is i...

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  9. If f(x)=((a+x)/(b+x))^(a+b+2x), then prove that f'(0)=[2log""(a)/(b)+(...

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  10. [(3,-2),(6,-k)] =A,also detA=0 then find k.

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  11. intcos^(- 1)sqrt(x/(a+x))dx

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  12. Evalute int (xdx)/(x^4-x^2+1)

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  13. Solve: ydx-(x+2y^2)dy=0.

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  14. In a certain culture the rate of increment of bactreria at any instant...

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  15. Evalute: int(0)^((pi)/(4)) log(1+tantheta)d theta.

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  16. From the definition of the definite integral, find the value of int(1...

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  17. Using calculus, find the maximum value of the function ((x)/(a))^x .

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  18. Using integration, prove that the area of the closed region bounded by...

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  19. If the staight line (x)/(h)+(y)/(k)=1touches the curve ((x)/(a))^n+((y...

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  20. Solve: xdy-ydx=sqrt(x^2+y^2)dx.

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