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If y=[tan^-1 x]^2, then prove that : (x^...

If `y=[tan^-1 x]^2`, then prove that : `(x^2 + 1)^2 y_2+2x(x^2+1) y_1 = 2`.

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PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If y = 500e^7x + 600e^-7x show that (d^2y/dx^2) = 49y

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  2. If e^y(x+1)=1 show that (d^2y/dx^2) = (dy/dx)^2 ਹੈ।

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  3. If y=[tan^-1 x]^2, then prove that : (x^2 + 1)^2 y2+2x(x^2+1) y1 = 2.

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  4. Verify Rolle’s theorem for the function f(x) = x^2 + 2x - 8, x in [-4,...

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  5. Examine if Rolle’s theorem is applicable to any of the following funct...

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  6. Examine if Rolle’s theorem is applicable to any of the following funct...

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  7. Examine if Rolle’s theorem is applicable to any of the following funct...

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  10. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

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  11. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

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  13. Differentiate w.r.t. x the function : sin^3x + cos^6 x

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  14. Differentiate w.r.t. x the function : (5x)^(3cos2x)

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  15. Differentiate w.r.t. x the function : sin^-1(xsqrtx), 0lexle1

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  18. Differentiate w.r.t. x the function : (logx)^logx, x>1

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  19. Differentiate w.r.t. x the function : cos(acosx+bsinx), for some const...

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  20. Differentiate w.r.t. x the function : (sinx - cosx)^(sinx-cosx), x lie...

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