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Evaluate lim(nrarrinfty)([x]+[2x]+[3x]+...

Evaluate
`lim_(nrarrinfty)([x]+[2x]+[3x]+......+[nx])/(n^2)`
where [.] denotes greatest integer function.

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. The graph of function y=f(x) has a unique tangent at (e^a,0), through ...

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  3. Evaluate lim(nrarrinfty)([x]+[2x]+[3x]+......+[nx])/(n^2) where [.] d...

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  4. Evaluate lim(xrarr0)(int0^(x^2) costdt)/(xsinx)

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  5. Evaluate lim(xrarr0)(x-int0^(x) cost^2dt)/(x^3-6x)

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  6. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

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  7. If alpha and beta be the roots of the quadratic equation ax^2+bx+c=0 t...

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  8. Let a=min{x^2+2x+3, x in R} and b=lim(thetararr0)(1-costheta)/(theta^2...

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  9. If f(x)={(2x+3, "when x" lt 0),(0, "when x"=0),(x^2+3, "when x"gt 0):}...

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  10. Let y=f(x) be defined parametrically as y=t^2+t|t|, x=2t-|t|, t in R, ...

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  11. Let f(x) be a continuous function defined for 1 le x le 3. If f(x) tak...

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  12. Find the points points of discontinuity of y=1/(u^2+u-2) where u=1/(x-...

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  13. If f(x)=[x], where [.] denotes greatest integer function. Then check t...

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  14. Let f(x)={({1+|sinx|}^(a//|sinx|), -pi//6ltxlt0),(b, x=0),(e^(tan2x...

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  15. Discuss the continuity of f(x)=[tan^(-1)x]

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  16. Examine the function, f(x)={(x-1, x lt 0),(1//4, x=0), (x^2-1, xg...

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  17. Show the function, f(x)={((e^(1//x)-1)/(e^(1//x)+1), "when x" le 0),...

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  18. A function f(x) is defined by, implies f(x)=f(x)={(([x^2]-1)/(x^2-1)...

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  19. Discuss the continuity of the function, f(x)=lim(nrarrinfty)(log(2+x)...

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  20. Discuss the continuity of f(x) where f(x)=lim(nrarrinfty)("sin" (pix)/...

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