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(i) If x=sin t, y=sin 2t then prove that...

(i) If `x=sin t`, `y=sin 2t` then prove that `(1-x^2)d^2y/dx^2-xdy/dx+4y=0`.
If `y=gof (x)` then find dy/dx.

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MODERN PUBLICATION-TEST PAPER 8-EXERCISE
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  2. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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  3. Find the interval in which y=(x-1)^2(x+2) is : (i) increasing (ii)...

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  4. Evaluate : int dx/(x(x^4+1))

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  5. Evaluate : int dx/sqrt (x^2+8x)

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  6. Evaluate : int(0)^(pi/2) e^x cos x dx .

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  7. From the differential equation whose general solution is y=asint+be^t.

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  8. Find the unit vector perpendicular to the plane ABC, where the positio...

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  9. Show that (vec(a)-vec(b))xx(vec(a)+vec(b))=2(vec(a)xxvec(b)).

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  10. The direction cosines of a straight line in two neighbouring positions...

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  11. Find the equation of the plane Passing through the intersection of the...

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  12. Find the equation of the straight line perpendicular to the line (x-2)...

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  13. Exaniming consistency and solvability, solve the following equations b...

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  14. Prove [[a^3-x^3,a^2,a],[b^3-x^3,b^2,b],[c^3-x^3,c^2,c]] = (a-b)(a-c)(b...

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  15. (i) If x=sin t, y=sin 2t then prove that (1-x^2)d^2y/dx^2-xdy/dx+4y=0....

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  16. Show that the radius of the right cicular cylinder of greatest curved ...

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  17. Find the solution of the differential equation x sin (y/x)dy =(y sin...

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  18. Find the area of the region included between the parabola y^(2)=2x and...

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  19. A variable plane is at a constant distance p from the origin and meets...

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