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If x=a(cost+tsint) and y=a(sint- tcost) ...

If `x=a(cost+tsint)` and `y=a(sint- tcost)` , find `(d^2y)/(dx^2)` .

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BANSAL-LIMITS AND DERIVATIVES-All Questions
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  2. If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+...

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  3. If x=a(cost+tsint) and y=a(sint- tcost) , find (d^2y)/(dx^2) .

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  10. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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

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  12. Evaluate find a and b if \ ("Lim")(x->0)(x(1+acosx)-bsinx)/(x^3)=1

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  13. ("Lim")(x->0)(e^xsinx-x-x^2)/(x^2+x-"ln"(1-x))

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  14. Evaluate: ("Lim")(x->0)(1+sinx-cosx+"ln"(1-x))/(xtan^2x) -1/2 (b)...

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  15. Evaluate: ("Lim")(x->0)((log)(secx/2)(cosx))/((log)(secx)(cos(x//2))) ...

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  16. Evaluate: ("Lim")(x->1)(x^x-x)/(x-1-lnx)

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  17. Evaluate: ("Lim")(x->0)(1-cosx cos2x cos3x)/(x^2)

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  18. Evaluate: ("Lim")(x->0)((cosa x)^(1//m)-(cosb x)^(1//n))/(x^2)

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  19. Evaluate: ("Lim")(x->0^+)("c o s e c"x)^(1/(lnx))

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  20. Evaluate: ("Lim")(x->pi//2)(secx)^(cotx)

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