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If x=acos theta+bsintheta and y=a sinthe...

If `x=acos theta+bsintheta and y=a sintheta-bcostheta,` then prove that `y^(2)(d^(2)y)/(dx^(2))-(dy)/(dx)+y=0`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If x = 2 cos theta - cos 2 theta, y = 2 sin theta - sin 2 theta, find ...

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  2. If x = a { cos t + log|tan t/2|} and y = a sin t, 0 < t < pi/2, find (...

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  3. If x=acos theta+bsintheta and y=a sintheta-bcostheta, then prove that ...

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  4. If y = x log (x/(a+bx)), prove that x^3 y 2 = (xy1 - y)^2

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  5. If x = g(t) and y = f(t), find (d^2y)/(dx^2) as a function of t.

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  6. If f(x) = |x|^3 show that f''(x) exists for all real x and find it.

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  7. Find the second derivative of the following functions: ax^3 + bx^2 +...

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  8. Find the second derivative of the following functions: a^x

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  9. Find the second derivative of the following functions: x sin x

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  10. Find the second derivative of the following functions: log (logx)

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  11. Find the second derivative of the following functions: e^(sinx)

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  12. Find the second derivative of the following functions: log(x+sqrt(x^...

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  13. Find the second derivative of the following functions: sin 3 x sin 6...

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  14. Find the second derivative of the following functions: x/(x^2 - 3x +...

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  15. If y = sin^(-1)x, then prove that (d^(2)y)/(dx^(2)) = (x)/((1 - x^(2...

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  16. If y = sin^-1x, then show that (1-x^2)(d^2y)/(dx^2)- x dy/dx = 0

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  17. If y = sin^-1x, prove that (1-x^2)y2 - x y1= 0

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  18. Find the second order derivative of the following functions If y = x...

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  19. Find the second order derivative of the following functions If y = a...

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  20. lf y=3e^(2x) +2e^(3x), prove that d^2y/dx^2 - 5dy/dx +6y =0.

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