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If y = Ae^(mx) + Be^(nx), Show that (d^2...

If `y = Ae^(mx) + Be^(nx)`, Show that `(d^2 /dx^2 y)-(m+n)dy/dx+mny = 0`

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PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If y = cos^-1x Find (d^2y/dx^2) in terms of y alone.

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  2. If y = 3 cos (log x) + 4 sin (log x) show that x^2 y2 + xy1 + y = 0

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  3. If y = Ae^(mx) + Be^(nx), Show that (d^2 /dx^2 y)-(m+n)dy/dx+mny = 0

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  4. If y = 500e^7x + 600e^-7x show that (d^2y/dx^2) = 49y

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

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

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

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

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

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

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  11. If f:[-5,5] rarr R is a differentiable function and if f'(x) does not...

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  12. Verify Mean Value Theorem, if f(x) = x^2-4x-3, in the interval [a, b],...

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

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

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  15. Differentiate w.r.t. x the function : (3x^2 - 9x + 5)^9

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

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

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

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  19. Differentiate w.r.t. x the function : cos^-1(x/2)/sqrt(2x+7), x lies b...

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  20. Differentiate w.r.t. x the function : cot^-1[(sqrt(1+sinx) + sqrt(1-si...

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