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If x=a (cos t + t sin t) and y = a (sin t - t cos t )`, find `(d^2x)/(dt^2),(d^2y)/(dt^2) and (d^2y)/(dx^2)`. Also mention the domain of validity.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find (d^2y)/(dx^2) if x= cos theta, y = a sin theta)

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  2. If x = a sin^3 theta, y = a cos^3 theta, find (d^2y)/(dx^2) at theta ...

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  3. If x=a (cos t + t sin t) and y = a (sin t - t cos t ), find (d^2x)/(dt...

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  4. Find (d^2y)/(dx^2) in the following If x = a (theta + sin theta) , y...

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  5. If x=(1-t^2)/(1+t^2), y=(2t)/(1+t^2), find (dy)/(dx) at x=2.

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  6. Verify Rolle's theorem for the following functions in the given interv...

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  7. Find the derivative of Following tan(log3x)

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  8. Find the derivative of Sin2x+Cosec5x

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  9. Find the derivative of cot2x-cos9x

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  10. Verify Rolle's theorem for the following functions in the given interv...

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  11. Verify the conditions of Rolle's Theorem in the followin problems. In ...

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  12. Verify Rolle's theorem for the following functions in the given interv...

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  13. Verify Rolle's theorem for the following functions in the given interv...

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  14. Verify Rolle's theorem for the following functions in the given interv...

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  15. Verify Rolle's theorem for the following functions in the given interv...

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  16. Verify Rolle's theorem for the following functions in the given interv...

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  17. Verify Rolle's theorem for the following functions in the given interv...

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  18. Verify Rolle's theorem for the following functions in the given interv...

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  19. Verify Rolle's theorem for the following functions in the given interv...

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  20. Verify Rolle's theorem for the following functions in the given interv...

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