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If y=tan^(-1)(cosx/(1+sinx)),then prove ...

If` y=tan^(-1)(cosx/(1+sinx)),`then prove that `dy/dx=-1/2`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

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  2. If 2y=x(1+(dy)/(dx)), then show that y(2) is a constant.

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  3. If y=tan^(-1)(cosx/(1+sinx)),then prove that dy/dx=-1/2

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  4. Examine the continuity of the following functions at indicated points....

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  5. If f(x+y)=f(x)f(y)for all real x,y,f(2)=3,f'(0)=1 then what is the val...

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  6. Find the area of the circle x^2+y^2=2ax.

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  7. intdx/(sqrtx-root(3)(x))(x=t^6)

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  8. Solve dy/dx+y/x=xy^2.

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  9. Evaluate int0^2abs(x^2+2x-3)dx

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  10. Evaluateint-2^2[x^2+3x+2]dx.

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  11. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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  12. Find the vector projection of veca=hati-hatj+hatk on vecb=3hati+hatj+3...

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  13. Show that the line passing through the points (a1,b1,c1) and (a2,b2,c2...

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  14. What is the number of line which are equally inclined to the axes?

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  15. Prove that (d)/(dx)[(sin2x+1/(cos^2x)]

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  16. If y=e^x+a^x+x^x, then find dy/dx at x=a

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  17. Show that the semivertical angle of a cone of given slant height is ta...

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  18. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

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  19. If a line in the space makes angles alpha, beta  and gamma  with the c...

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  20. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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