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show that lim(nrarr0)(root(3)(n+1)-1)/n=...

show that `lim_(nrarr0)(root(3)(n+1)-1)/n=1/3`

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UNITED BOOK HOUSE-MCQ-EXERCISE
  1. Show that the eccentricities of the two hyperbolas x^2/16-y^2/9=1and x...

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  2. Find the co-ordinates of the point of trisection of the line segment j...

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  3. show that lim(nrarr0)(root(3)(n+1)-1)/n=1/3

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  4. If f(x)=x|x|,prove that f'(x)=2|x|.

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  5. if lim(xrarra)f(x)=lim(xrarra)g(x),then whether f(x)=g(x) is always tr...

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  6. From the following array, find out the mean deviation. 7,9,16,24,26,3...

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  7. Define ‘mutually exclusive’ and ‘mutually exhustive’ events and give e...

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  8. Two dice are thrown simultaneously. Find the probability that the sum ...

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  9. For any three sets A,B and C ,prove that A-(BcupC)=(A-B)cap(A-C).

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  10. Find the domain of definition of f(x)=loge ((1-x)/(1+x)) Further show ...

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  11. sintheta=ksin(theta+phi).show that tan(theta+phi)=(sinphi)/(cosphi-K)

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  12. Prove that tan 20^@tan 40^@ tan 60^@ tan 80^@ = 3

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  13. If a sinalpha+bcosalpha=c and a cosecalpha+bsecalpha=c show thatsin2al...

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  14. Prove that 4sin27^@=sqrt(5+sqrt5)-sqrt(3-sqrt5)

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  15. Solve :tanx+tany=1,x+y=pi//4

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  16. If a^4+b^4+c^4+a^2b^2=2c^2(a^2+b^2),, then show thatangleC=60^@or120^@

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  17. Prove using principle of mathematical induction that sum of the cube t...

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  18. If x+iy=((a+ib)/(c+id))^(1//2),show that (x^2+y^2)=(a^2+b^2)/(c^2+d^2)

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  19. If one of the root of the equation px^2 + qx + r = 0 is the cube of th...

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  20. Solve graphically the following system of linear inequations - x - y l...

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