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If y=xlog(x/(a+bx)), then prove that x^3...

If `y=xlog(x/(a+bx))`, then prove that `x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2`

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MOTION-METHOD OF DIFFERENTIATION-EXERCISE - 3
  1. Differentiate the given functions w.r.t.x. (ln"x")^(cos"x") (ii) x^x-...

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  2. If cosx/2dotcosx/(2^2)dotcosx/(2^3)oo=(sinx)/x , then find the value o...

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  3. If y=xlog(x/(a+bx)), then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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  4. If y = tan^(-1)(u/sqrt(1-u^2)) and x = sec^(-1)(1/(2u^2-1)), u in (0...

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  5. Differentiate (sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)) w,r,...

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  6. Let f(x)=x+1/(2x+1/(2x+1/(2x+ . . . oo)) Compute the value of f(100)*f...

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  7. If y=x+1/(x+1/(x+1/(x+ . . . oo)) prove that dy/dx=y=1/(2-x/(x+1/(x+1/...

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  8. If f(x)=2ln(x-2)-x^2+4x+1, then find the solution set of the inequalit...

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  9. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

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  10. Evaluate ("Lim")(x->0)(xcosx-"ln"(1+x))/(x^2)

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  11. If Lim(xrarr0)(a^(x)-x^(a))/(x^(x)-a^(a))=-1 , find 'a'

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  12. Lim(xrarr0)(1+sinx-cosx+ln(1-x))/(x.tan^(2)x)

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  13. If ("Lim")(x->0)(asinx-b x+c x^2+x^3)/(2x^2dotln(1+x)-2x^3+x^4) exists...

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  14. If lim(x->0)(1-cosx.cos2x.cos3x ....cosn x)/x^2 has the value equal to...

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  15. Let f(x) = x^2-4x-3, x > 2 and let g be the inverse of f. Find the val...

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  16. If f:R->R is a function such that f(x)=x^3+x^2f''(2)+f'''(3) for all x...

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  17. If x=at^3 and y =bt^2, where t is a parameter, then prove that (dy)/(d...

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  18. If f(x)=|[(x-a)^4, (x-a)^3, 1] , [(x-b)^4, (x-b)^3,1] , [(x-c)^4, (x-c...

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  19. f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x...

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  20. Find a polynomial function f(x) such that f(2x) = f'(x) f ''(x).

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