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Find the integral value of `n` for which `lim_(x->0)(cos^2x-cosx-e^xcosx+e^x-(x^3)/2)/(x^n)` is a finite nonzero number

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RESONANCE DPP-JEE MAINS-All Questions
  1. Let u=int0^1("ln"(x+1))/(x^2+1)dxa n dv=int0^(pi/2)ln(sin2x)dx ,t h e ...

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  2. int(-1/(sqrt(3)))^(1/(sqrt(3)))(cos^(-1)((2x)/(x^2+1))+tan^(-1)((2x)/(...

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  3. Find the integral value of n for which lim(x->0)(cos^2x-cosx-e^xcos...

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  4. If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) i...

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  5. If vec a= hat i+ hat j+ hat k , vec b=4 hat i+3 hat j+4 hat k and ve...

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  6. 1)int(-pi/2)^pi sin^(-1) (sinx) dx 2)int(-pi/2)^(pi/2) (-pi/2)/(sqr...

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  7. if f(x) = lim(n->oo) 2/n^2(sum(k=1)^n kx)((3^(nx)-1)/(3^(nx)+1)) where...

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  8. int(sqrt(1+x^2)-x)^n dx

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  9. The expression [(1+sin(pi/8)+icos(pi/8))/(1+sin(pi/8)-icos(pi/8))]^8 i...

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  10. if the roots of the equation z^(2) + ( p +iq) z + r + is =0 are real ...

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  11. The expression in the vector form for the point vec r1 of intersectio...

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  12. If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...

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  13. If int0^a(dx)/(sqrt(x+a)+sqrt(x))=int0^(pi/8)(2tantheta)/(sin2theta)dt...

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  14. The area of the closed figure bounded by x=-1,x=2,a n d y={-x^2+2,xlt...

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  15. "S o l v e"int0^(pi/2)(cosx)/((1+sinx)(2+sinx))dx

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  16. If Sn=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n^2-4))++1/(sqrt(3n^2+2n-1)),n ...

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  17. The function f satisfies the functional equation 3f(x)+2f((x+59)/(x-1...

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  18. The reflection of the point vec a in the plane vec rdot vec n=q ...

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  19. The equation of tangent to the curve y=int(x^2)^(x^3)(dt)/sqrt(1+t^2) ...

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  20. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

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