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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-TANTIA HIGH SCHOOL-EXERCISE
  1. Evaluate :lim(xrarr1)(x+x^2+x^3+...+x^n-n)/(x-1)

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  2. If y=(1-x)(2-x)(3-x)…(n-x),find dy/dx

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

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  4. For any two sets A,B ,prove that (AcapB)'=A'cupB'

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  5. If (cot(alpha-beta))/cotalpha+(cos^2gamma)/(cos^2alpha)=1show that tan...

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  6. If sinx-siny=a and cosx+cosy=b,prove that tan((x+y)/2)=+-sqrt((4-a^2-b...

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  7. Prove that sintheta/(cos3theta)+(sin3theta)/(cos9theta)+(sin9theta)/(c...

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  8. If tan (theta/2)=tan^3 (phi/2)and tanphi=2tanalpha,then prove that the...

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  9. If a,b are real and a^2+b^2=1,then prove that the equation.(1-ix)/(1+i...

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  10. If the roots of the equation x^2+2px+q=0and x^2+2qx+p=0where p!=q.Diff...

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  11. Prove that the product of any r consecutive natural number is always d...

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  12. Find the rank of the word LAKE,when the letters are arranged as in a d...

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  13. The sum of three numbers in G.P is 70.If the two extremes be mulitipli...

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  14. A ray of light comming from (1, 2) to the x axis at A and reflecting w...

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  15. The equation of a side of a rectangle is 4x+7y+5=0 and the two vertice...

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  16. Find the equation of the circle described on the common chord of the c...

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  17. Find the equation of the parabola whose focus is at the origin and the...

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  18. Evaluate :lim(xrarr0)(sqrtcosx-root(3)(cosx))/(sin^2x)

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  19. Find from first principle,the derivative of sqrttanx

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  20. If y=sqrt(x/m)+sqrt(m/x),Prove that 2xydy/dx=x/m-m/x

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