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If y = a sin (log x) + b cos (log x), th...

If `y = a sin (log x) + b cos (log x)`, then prove that : `x^2 d^2y/dx^2+ x dy/dx+ y = 0`.

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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. Differentiate cos^(-1) ((1 - x^2)/(1 + x^2)) , 0 lt x lt 1. w.r.t.x

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  2. Diferentiate tan^(-1)((2x)/(1 - x^2)) w.r.t.x.

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  3. If y = a sin (log x) + b cos (log x), then prove that : x^2 d^2y/dx^2+...

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  4. If y=sin(msin^-1x), prove that (1-x^2)y2-xy1+m^2y=0

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  5. Discuss the continuity of f(x) = 0 at x = 0 if f(x) = {{:((sqrt(1 + ...

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  6. Discuss the continuity of following at x = 0 if f(x) = {{:((sqrt(1 +...

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  7. Determine the value of constant k so that the function f(x) = {{:((x...

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  8. Determine the constant k, so that the function f(x) = {{:((x^2- 9)/(...

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  9. Examine the continuity of the following function at x = 2 : f(x) = {...

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  10. Examine the continuity of the following function at x = 2 : f(x) = {...

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  11. Differentiate the following w.r.t.x y = log(x+4+sqrt(x^2 +8x+4))

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  12. Differentiate the following w.r.t.x y= log(x+2+sqrt(x^2 + 4x+1))

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  13. y = sqrt(cos x + sqrt(cosx + sqrt(cosx + ...."to " oo))) prove that (2...

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  14. y = sqrt(sin x + sqrt(sinx + sqrt(sinx + ....1 oo))) prove that (2y - ...

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  15. y = sqrt(tan x + sqrt(tanx + sqrt(tanx + ...."to" oo))) prove that (2y...

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  16. If sin y = x cos (a + y), prove that (dy)/(dx) = (cos^2 (a + y))/(cos ...

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  17. x = a (theta - sin theta), y = a (1 + cos theta) find dy/dx

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  18. If y = (sin x)^(cos x) find (dy)/(dx).

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  19. If y = (cos x)^(sin x) find (dy)/(dx)

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  20. Differentiate cos^(-1)((1 - x^2)/(1 + x^2)) w.r.t. tan^(-1)x.

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